Determine the vapor pressure of a solution at 55 °C that contains 34.2 g NaCl in 375 g of water. The vapor pressure of pure water at 55 °C is 118.1 torr. The van't Hoff factor for NaCl is 1.9

Answer:

[HNO₃] = 45.4 m

Explanation:

We need to be organized to solve this:

Solute: HNO₃

Solvent: Water

Solution: Mass of solute + Mass of solvent

Density → For the solution → Solution mass / Solution Volume

M → moles of solute / 1L of solution

Let's use density to determine solution mass

1.42 g/mL = Solution mass / 1000mL → Solution mass = 1420 g

Let's determine the moles of the solute (HNO₃)

Moles . molar mass → 16.7 mol . 63 g/mol = 1052.1 g

Now we have solution mass and solute mass; let's find out solvent mass.

Solvent mass = Solution mass - Solute mass → 1420 g - 1052.1 g = 367.9 g

Let's convert the solvent mass to kg → 367.9 g . 1kg / 1000 g = 0.6379 kg

Molality → Moles of solute / 1kg of solvent → 16.7 mol / 0.6379 kg = 45.4 m

Answer:

53.4 % is the percent yield

Explanation:

This is the reaction:

C₆H₆ + Cl₂ → C₆H₅Cl + HCl

First of all we need to know the moles of benzene we used

39 g . 1 mol / 78 g = 0.5 moles

Ratio is 1:1 so 1 mol of benzene produces 1 mol of chloride

0.5 moles of chloride were produced by 0.5 moles of benzene

We must calculate the mass of chloride we produced

0.5 mol . 112.45 g / 1 mol = 56.2g

Let's calculate the  percent yield

(Yield produced / Theoretical yield ) . 100

(30 g / 56.2 g) . 100 = 53.4 %

Answer:

53.4%

ut quest

Answer: Option B. oxidized

Explanation:

Answer: The main group metal produce a basic solution in water and the reaction is [tex]MO+H_2O\rightarrow M(OH)_2[/tex]

Explanation:

Main group elements are the elements that are present in s-block and p-block.

The metals that are the main group elements are located in Group IA, Group II A and Group III A.

Oxides are formed when a metal or a non-metal reacts with oxygen molecule. There are two types of oxides which are formed: Acidic oxides and basic oxides.

When a metal oxide is reacted with water, it leads to the formation of a base.

The general formula of the oxide formed by Group II-A metals is 'MO'

The chemical equation for the reaction of metal oxide of Group II-A and water follows:

[tex]MO+H_2O\rightarrow M(OH)_2[/tex]

Hence, the main group metal produce a basic solution in water and the reaction is [tex]MO+H_2O\rightarrow M(OH)_2[/tex]

The reaction of a main-group metal oxide in water generally produces a basic solution. This is true for Group 2A(2) oxides, with beryllium and magnesium as exceptions. An example is the reaction of calcium oxide with water, producing calcium hydroxide.

The reaction of a main-group metal oxide in water typically produces a basic solution, this is particularly true for Group 2A(2) oxides. The Group 2A metals, also known as the alkaline earth metals, react with water to produce basic metal hydroxides and hydrogen gas. However, it is important to note the exceptions of beryllium and magnesium oxides which do not readily react with water. An example of a group 2A metal oxide reacting with water can be seen with calcium oxide (CaO):

CaO (s) + H2O (l) --> Ca(OH)2 (aq)

This reaction produces calcium hydroxide, a basic solution in water.

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To determine the number of moles of air required for the combustion of isooctane, you can use the ratio of moles of air to moles of oxygen in air. The moles of air can be calculated by multiplying the moles of oxygen by the ratio and the number of moles of isooctane.

To determine the number of moles of air required for the combustion of 5.00 mol of isooctane, we need to consider the balanced chemical equation for the combustion reaction. From the equation, we can see that 1 mole of isooctane requires 13.5 moles of oxygen. Since air is 21.0% oxygen by volume, we can calculate the moles of air required by converting the moles of oxygen to moles of air.

To do this, we multiply the moles of oxygen by the ratio of moles of air to moles of oxygen. The ratio is obtained by dividing the volume percentage of oxygen in air (21.0%) by the volume percentage of oxygen (100%). Finally, we multiply this by the number of moles of isooctane (5.00 mol) to find the moles of air required.

moles of air = (moles of oxygen) x (volume percentage of oxygen in air/volume percentage of oxygen) x (moles of isooctane)

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Binary acids can be ranked based on the electronegativity and size of the non-metal in the acid.

The strength of binary acids can be determined by looking at the electronegativity and size of the non-metal in the acid. Higher electronegativity and smaller size result in stronger acids. From the given compounds, we can rank them as follows:

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Answer:

A) homotopic and B) enantiotopic

Explanation:

Protons chemically equivalent are those that have the same chemical shift, also if they are interchangeable by some symmetry operation or by a rapid chemical process.

The existence of symmetry axes, Cn, that relate to the protons results in the protons being homotopic, that is chemically equivalent in both chiral and aquiral environments.

The existence of a plane of symmetry, σ, makes the protons related by it, are enantiotopic and these protons will only be equivalent in an aquiral medium; if the medium is chiral both protons will be chemically NOT equivalent. The existence of a center of symmetry, i, in the molecule makes the related protons through it enantiotopic and therefore chemically only in the aquiral medium.

Diastereotopic protons cannot be interconverted by any symmetry operation and they are different, with different chemical displacement.

Homotopic and enantiotopic protons are chemically equivalent, while diastereotopic protons are not.

option A and B are chemically equivalent

In organic chemistry, protons in a molecule can be classified into different types based on their position and chemical environment. Among the given options, the type of protons that are chemically equivalent are homotopic and enantiotopic.

Homotopic protons are protons that have an identical chemical environment and can be interchanged with each other without affecting the molecule's structure or properties. Enantiotopic protons are protons that have an identical chemical environment but their interchange leads to the formation of a stereoisomer.

Diastereotopic protons, on the other hand, have different chemical environments and are not chemically equivalent.

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For each group mentioned, the number of unpaired electrons can be determined by considering their electron gain or loss.

(a) Elements of group 1 need to lose one electron, elements of group 14 need to gain 4 electrons, and elements of group 17 need to gain 1 electron.

(b) Elements of group 1 need to lose 1 electron, elements of group 14 and 17 need to gain 1 electron each.

(c) Elements of group 1 need to lose 2 electrons, elements of group 14 need to gain 4 electrons, and elements of group 17 need to gain 1 electron.

(d) Elements of group 1 need to gain 1 electron, elements of group 14 need to lose 4 electrons, and elements of group 17 need to lose 1 electron.

Answer:

The Pauli exclusion principle was developed by Austrian physicist Ernst Pauli in 1925.  This principle of quantum says that two electrons in an atom cannot have all four equal quantum numbers .

Explanation:

This fact would explain that electrons are dispersed in layers or levels around the nucleus of the atom and therefore, atoms that have more electrons occupy more space, because the number of layers of which the atom consists increases. The maximum number of electrons that a layer or level can have is 2n ^ 2.

In order to fully describe the electron within the hydrogen atom, we need to enter a fourth quantum number to those already known. Said fourth quantum number is represented by the letters ms, and is known as the quantum number of spin, which is closely related to the magnetic properties of electrons. The quantum number ms can only have two different values, +1/2 or -1/2. To electrons whose values ​​of ms are equal, it is said that they have what is known as parallel spins, however, if the values ​​that present more are different it is said that they have opposite spins or also called antiparallels.

In order to describe an orbital, three quantum numbers (the numbers n, l and ml) are needed, at the same time that an electron that is in an atom is given by a combination of four quantum numbers, the main three plus the number ms . Pauli's exclusion principle tells us that in an atom it is impossible for two electrons to coexist with the four identical quantum numbers. According to this principle, in an atomic type orbital, which is determined by the quantum numbers n, l, and ml, there can only be two electrons: one of them with a positive spin +1/2 and another with its opposite spin negative -1/2.

Then we say that each of the types of orbitals can only contain 2 electrons at most, which must necessarily have opposite spins. These electrons will have all their equal quantum numbers, and will only differ in the quantum number ms (spin).

Explanation:

Technically the exclusion principle says that electrons with the same orbital designations must have different spin. ... For a given level (n), the sublevels in H have the same energy, whereas in many-electron, species, the sublevels are staggered in energy.

Explanation:

Ethanethiol is an organosulphur compound which had an alkyl group(CnH2n+1) and a -thiol group (-SH). A thiol group like an hydroxyl group has its Oxygen replaced with sulphur.

Ethanethiol shows little association of its -SH group with the water molecules by hydrogen bonding; both with water molecules and among themselves. Hence why they are less soluble in water or slightly soluble in water.

Ethanol is an organic compound which the general formula of CnH2n+1OH. Ethanol is soluble in water because of the reaction of the -OH group with the water molecules to form hydrogen bonds.

Note that as the alkyl chain increases, Solubility decreases. This is because the alkyl chain forms the hydrophobic surface of the molecule due to its non-interaction of the water molecules to form hydrogen bond.

Ethanol is completely miscible with water due to its polar nature and ability to form strong hydrogen bonds with water. However, ethanethiol is only partially soluble because it forms weaker hydrogen bonds with water due to its less polar sulfhydryl group.

The miscibility and solubility of substances depend on the principle that 'like dissolves like'. This means that polar substances dissolve well in other polar substances, while non-polar substances dissolve well in other non-polar substances. Ethanol (C2H5OH) is a polar molecule because it contains a hydroxyl group (-OH), which forms hydrogen bonds with water, another polar substance. This makes ethanol completely miscible with water. On the other hand, ethanethiol (C2H5SH) contains a sulfhydryl group (-SH), which is less polar than the hydroxyl group and forms weaker hydrogen bonds with water. As a result, ethanethiol is only partially soluble in water.

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According to the Law of Multiple Proportions, the mass ratio 1:0.7391 (option 'b') follows the formula because the ratios are related by a simple whole number.

The Law of Multiple Proportions states that when two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.

For Compound A, the mass ratio of element X to element Y is 1.000 g of X for every 2.100 g of Y. For the Law of Multiple Proportions to hold for compounds A and B, the mass ratio of X to Y in compound B must be a simple multiple or fraction of the 1.000 g: 2.100 g ratio found in compound A.

Looking at the choices given: the only ratio that is a simple multiple of the ratio for Compound A is choice 'b', with a ratio of 1.000 g X: 0.7391 g Y. This is because 2.100 g divided by 0.7391 g equals approximately 3, a small whole number.

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The size of an ion is determined by the effective nuclear charge and the number of electrons in the ion. In isoelectronic ions, the size decreases with increasing effective nuclear charge. In ions with the same number of electrons, the size increases with increasing atomic number.

(a) In this set, the ions are all isoelectronic, meaning they have the same number of electrons. Therefore, their sizes are determined by the effective nuclear charge. The effective nuclear charge increases from Se²⁻ to S²⁻ to O²⁻ because the number of protons in the nucleus increases. So, the sizes of the ions decrease from Se²⁻ > S²⁻ > O²⁻.

(b) In this set, the ions have different numbers of electrons. The size of an ion generally increases with the addition of electrons. So, the sizes of the ions decrease from I⁻ > Te²⁻ > Cs⁺.

(c) In this set, the ions have the same number of electrons but different atomic numbers. The size of an ion generally increases with increasing atomic number. So, the sizes of the ions decrease from Cs⁺ > Sr²⁺ > Ba²⁺.

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The size of an ion is determined by the number of electrons surrounding it. In each set, the size of the ions decreases as you move along the set. The order of decreasing size for each set is explained based on the position of the elements on the periodic table.

(a) Se²⁻, S²⁻, O²⁻: The size of an ion is determined by the number of electrons surrounding it. As you move down a group on the periodic table, the size of the ions generally increases. Therefore, the order of decreasing size is O²⁻, S²⁻, Se²⁻.

(b) Te²⁻, Cs⁺, I⁻: In this set, the ionic size increases from Te²⁻ to I⁻. This is due to the decrease in the number of protons in the nucleus as you move down the periodic table. Cs⁺ is significantly smaller than Te²⁻ and I⁻ due to the removal of an electron.

(c) Sr²⁺, Ba²⁺, Cs⁺: Again, the size of the ions increases as you move down the periodic table. Therefore, the order of decreasing size is Cs⁺, Sr²⁺, Ba²⁺.

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In cellular respiration, electrons are transferred through the electron transport chain, with oxygen as the final acceptor in aerobic respiration, or alternate acceptors in anaerobic conditions, resulting in ATP production or NAD⁺ regeneration, respectively.

When electrons move through a series of electron acceptor molecules in cellular respiration, they travel along the electron transport chain (ETC), which is a series of chemical reactions that occur within the inner membrane of mitochondria in eukaryotic cells, or on the cell membrane in prokaryotic cells. In aerobic respiration, the final electron acceptor is an oxygen molecule (O₂), leading to the production of water and the generation of ATP through the process of oxidative phosphorylation. If oxygen is not available, the cell may undergo anaerobic respiration or fermentation, utilizing an organic or inorganic molecule as the final electron acceptor and, in the case of fermentation, regenerating NAD⁺ from NADH to permit glycolysis to continue.

The speed of sound in different mediums varies based on their properties. In air at 20 oC, the speed of sound is approximately 343 m/s. In helium, it is approximately 972 m/s, and in natural gas (methane), it is approximately 454 m/s.

The speed of sound in a medium depends on the properties of that medium. In general, sound travels faster in materials with higher densities and elastic properties. The equation to calculate the speed of sound in a medium is given by v = sqrt(E/p), where v is the speed of sound, E is the elastic modulus, and p is the density of the medium.

(a) In air at 20 oC, the speed of sound is approximately 343 m/s.

(b) In helium at 20 oC, the speed of sound is approximately 972 m/s.

(c) In natural gas (methane) at 20 oC, the speed of sound is approximately 454 m/s.

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Final answer:

The speed of sound in air at 20.0°C is 343 m/s. For other gases like helium and methane at the same temperature, their speeds of sound are higher due to their lower molecular masses. Helium has a much higher speed of sound, while methane's speed of sound is closer to but slightly higher than air.

Explanation:

The speed of sound in air at a given temperature can be calculated using the following formula, where °C represents degrees Celsius:

v = 331 m/s + (0.6 m/s/°C) × temperature

For air at 20.0°C, the speed of sound is:

v = 331 m/s + (0.6 m/s/°C) × 20.0°C

v = 331 m/s + 12 m/s

v = 343 m/s

For other gases like helium and methane at the same temperature, their speeds of sound are higher due to their lower molecular masses compared to air.

The speed of sound in helium and methane can be determined from tables or calculated using specific formulas accounting for the properties of these gases.

Answer: Ioniç bond is also called electrovalent bond. It involves the transfer of electrons from positively charged ions to negatively charged ions. covalent bond is a type of chemical bond that involves electrons sharing by atoms of a molecule in order to achieve a stable electronic configuration.. Metallic bond is a type of chemical bond that forms between metal atoms and it occurs when positive metal ions are attracted to a negatively charged electron that are not associated with a single atom. The differences can be seen in the definitions above.

Pauli exclusion principle states that electrons which are identical cannot have the same quantum state.

Ionic bonding involves transfer of electrons. Covalent bonding is the sharing of electrons between atoms. Metallic bonding involves free electrons shared among positively charged ions. The Pauli Exclusion Principle dictates that no two electrons can have identical quantum numbers.

(a) Ionic, covalent, and metallic bonding are principal types of atomic bonding. Ionic bonding includes transfer of electrons from one atom to another, resulting in the formation of positive and negative ions, which are held together by electrostatic forces. In covalent bonding, electrons are shared between atoms. This happens usually between non-metals. Lastly, metallic bonding involves the sharing of free electrons among a lattice of positively charged ions, commonly seen in metals.

(b) The Pauli Exclusion Principle states that no two electrons in an atom can have identical quantum numbers. This means that each electron in an atom has a unique state, and it is distinguished by its quantum numbers.

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Answer:

a. 108.19 amu

Explanation:

Isotopes are atoms of the same element, which have the same number of protons and electrons, but a different number of neutrons, and, because of that, different masses.

The atomic mass (M) in the periodic table is a ponderation of the masses of all isotopes found in nature. Thus, it is the summation of the percent multiplied by the mass of each isotope, so:

M = 0.5184*106.90509 + 0.4846*108.90476

M = 108.19 amu

amu = atomic mass unit.

The atomic mass of silver is 108.19 amu.

Isotopes are each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties.

The atomic mass of an element is a weighted average of the masses of its isotopes, considering their natural abundances. We can calculate the atomic mass of silver using the following expression.

[tex]m = \frac{\Sigma m_i \times ab_i }{100}[/tex]

where,

[tex]m = \frac{106.90509 amu \times 51.84 + 108.90476 amu \times 48.46 }{100} = 108.19 amu[/tex]

The atomic mass of silver is 108.19 amu.

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Answer:

V2 = 1/4

Explanation: P1 = 1; P2 = 2; V1 = 1/2; V2 = ?

P1*V1 = P2*V2

∴ V2 = P1*V1/P2 = {1 X 1/2}/2 = 1/4

Answer:

(a) Ba < Sr < Ca

(b) B < N < Ne

(c) Rb < Se < Br

(d) Sn < Sb < As

Explanation:

The weak intermolecular forces which can arise either between nucleus and electrons or between electron-electron are known as dispersion forces. These forces are also known as London dispersion forces and these are temporary in nature.

Dipole-dipole interactions are defined as the interactions that occur when partial positive charge on an atom is attracted by partial negative charge on another atom.

When a polar molecules produces a dipole on a non-polar molecule through distribution of electrons then it is known as dipole-induced forces.

Hydrogen bonding is defined as a bonding which exists between a hydrogen atom and an electronegative atom like O, N and F.

Chemical formula of acetone is [tex]CH_{3}COCH_{3}[/tex]. Due to the presence of oxygen atom there will be partial positive charge on carbon and a partial negative charge on oxygen atom. Hence, dipole-dipole forces will exist in a molecule of acetone.

Whereas hydrogen bonding will exist in a molecule of ethanol ([tex]CH_{3}CH_{2}OH[/tex]). Since, hydrogen atom is attached with electronegative oxygen atom.

Whereas London dispersion forces will also exist in both acetone and ethanol molecule.

Following numbers should be dialed:

The display of the P-10 pipette consists of three digits: tens, ones, and tenths. These digits represent different places in the measurement scale. Here's how you would set it for a volume of 3.7 µL:

Tens Section (Leftmost Digit - Tens Place):

Dial in the digit 3. This represents 3 tens of microliters (µL). Essentially, it sets the pipette to 30 µL.

Ones Section (Middle Digit - Ones Place):

Dial in the digit 7. This represents 7 ones of microliters (µL).

Tenths Section (Rightmost Digit - Tenths Place):

Dial in the digit 0. This represents 0.1 µL. However, for your measurement of 3.7 µL, you don't need to adjust this digit, as you don't have any tenths to add.

Putting it all together:

Tens: 3 (30 µL)

Ones: 7 (7 µL)

Tenths: 0 (0.1 µL, but not needed in this case)

So, with the tens set to 3 and the ones set to 7, you have dialed in a total volume of 37 µL.

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Final answer:

For measuring a volume of 3.7 L with a micropipette, it’s not feasible using a P-10 pipettor due to its limited range. If the intended volume is 3.7 µL, dial 037 into the P-10 display. It's essential to use the pipettor within the correct volume range to avoid damage.

Explanation:

To measure a volume of 3.7 L (3700 mL) using a P-10 micropipette, which has a maximum volume of 10 µL (0.01 mL), would not be possible because the micropipette's volume range is much smaller than the volume you need to measure. However, if you meant to measure 3.7 µL, the numbers to dial on the P-10 display would be 037, indicating that you need to measure 3.7 µL. You should rotate the volume adjustment knob until the display shows these three digits. It is crucial to operate within the pipettor's specified volume range for accuracy and to prevent damage to the equipment.

Caution: Never turn the indicator dial beyond the micropipette's volume limits. To measure volumes accurately with a micropipette, ensure you are using the correct model for the desired volume range and adjust the dial accordingly. Using the P10 model, you can measure volumes as small as 1 µL up to 10 µL, which is its upper volume limit. Always consult the pipettor's manual or your lab guidelines when unsure about how to correctly set the volume on the micropipette.

Final answer:

The equilibrium concentrations for CO and Cl₂ at 600 K are 0.540 M, and for COCl₂, it is 0.320 M, calculated using the equilibrium expression and the equilibrium constant (Kc).

Explanation:

To solve for the equilibrium concentrations of the substances involved in the reaction CO(g) + Cl₂(g) ⇌ COCl₂(g), we will use the provided equilibrium constant (Kc) and the initial concentrations of the reactants.

Let's let x be the amount of CO and Cl₂ that react to form COCl₂ at equilibrium. The initial concentration of CO and Cl₂ is 0.430 mol/0.500 L = 0.860 M.

At equilibrium, the concentrations are 0.239 M for both CO and Cl₂, and 0.621 M for COCl₂.

The equilibrium constant and initial concentrations were used to find these values. This calculation involves solving a quadratic equation.

To determine the concentrations of CO, Cl₂, and COCl₂ at equilibrium for the reaction CO(g) + Cl₂(g) ⇌ COCl₂(g), we start with the initial moles of each reactant and use the equilibrium constant, Kc.

Given:

First, calculate the initial concentrations: [CO]° = [Cl₂]° = (0.430 mol) / (0.500 L) = 0.860 M.

Let 'x' be the change in concentration of CO and Cl₂.

At equilibrium:

Set up the equilibrium expression:

Kc = [COCl]₂/ ([CO] [Cl₂]) = 4.95

4.95 = x / ((0.860 - x) (0.860 - x))

Solving for 'x' involves solving the quadratic equation: x = 0.621 M.

Therefore, at equilibrium:

To find the de Broglie wavelength of an alpha particle, use the equation λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum. To find the uncertainty in position, use the uncertainty principle, which states that Δx * Δp >= h.

To calculate the de Broglie wavelength of an alpha particle, we can use the equation:

λ = h / p

where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 J*s), and p is the momentum of the particle. The momentum can be calculated using the equation:

p = m * v

where m is the mass of the particle and v is its velocity. By substituting the given values into the equations, we can find the de Broglie wavelength of the alpha particle.

To calculate the uncertainty in the position of the alpha particle, we can use the uncertainty principle, which states that the product of the uncertainty in position (Δx) and the uncertainty in momentum (Δp) is greater than or equal to Planck's constant:

Δx * Δp >= h

By substituting the given uncertainty in the velocity into the momentum equation, we can calculate the uncertainty in momentum and then find the uncertainty in position.

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(a) The de Broglie wavelength of the alpha particle is [tex]\( {6.61 \times 10^{-15} \text{ m}} \).[/tex]

(b) The uncertainty in the position of the alpha particle is [tex]\( {3.31 \times 10^{-16} \text{ m}} \).[/tex]

To solve this problem, we'll use the principles of quantum mechanics, specifically relating to the de Broglie wavelength and the Heisenberg uncertainty principle.

Given:

Mass of the alpha particle, [tex]\( m = 6.6 \times 10^{-24} \) g[/tex]

Velocity of the alpha particle, [tex]\( v = 3.4 \times 10^7 \) mi/h[/tex]

Uncertainty in velocity, [tex]\( \Delta v = 0.1 \times 10^7 \) mi/h[/tex]

(a) de Broglie Wavelength Calculation:

The de Broglie wavelength [tex]\( \lambda \)[/tex] of a particle is given by:

[tex]\[ \lambda = \frac{h}{p} \][/tex]

where ( h ) is the Planck constant and ( p ) is the momentum of the particle.

First, convert the velocity from miles per hour to meters per second:

[tex]\[ v = 3.4 \times 10^7 \text{ mi/h} \times \frac{1609.34 \text{ m}}{1 \text{ mi}} \times \frac{1 \text{ h}}{3600 \text{ s}} \][/tex]

[tex]\[ v \approx 1.52 \times 10^7 \text{ m/s} \][/tex]

Next, calculate the momentum ( p ):

[tex]\[ p = m \cdot v \][/tex]

[tex]\[ p = 6.6 \times 10^{-24} \text{ g} \times 1.52 \times 10^7 \text{ m/s} \][/tex]

[tex]\[ p \approx 1.0032 \times 10^{-16} \text{ g} \cdot \text{m/s} \][/tex]

Now, calculate the de Broglie wavelength \( \lambda \):

[tex]\[ \lambda = \frac{h}{p} \][/tex]

Planck constant [tex]\( h = 6.626 \times 10^{-34} \) J·s.[/tex]

Convert the momentum to kg·m/s for consistent SI units:

[tex]\[ p \approx 1.0032 \times 10^{-19} \text{ kg} \cdot \text{m/s} \][/tex]

Now calculate [tex]\( \lambda \):[/tex]

[tex]\[ \lambda = \frac{6.626 \times 10^{-34} \text{ J·s}}{1.0032 \times 10^{-19} \text{ kg·m/s}} \][/tex]

[tex]\[ \lambda \approx 6.61 \times 10^{-15} \text{ m} \][/tex]

(b) Uncertainty in Position Calculation:

According to the Heisenberg uncertainty principle:

[tex]\[ \Delta x \cdot \Delta p \geq \frac{\hbar}{2} \][/tex]

Where [tex]\( \hbar = \frac{h}{2\pi} \)[/tex] is the reduced Planck constant.

To find [tex]\( \Delta x \),[/tex] we use the uncertainty in momentum [tex]\( \Delta p \),[/tex] which can be approximated as [tex]\( \Delta p \approx m \cdot \Delta v \):[/tex]

[tex]\[ \Delta p = 6.6 \times 10^{-24} \text{ g} \times 0.1 \times 10^7 \text{ mi/h} \times \frac{1609.34 \text{ m}}{1 \text{ mi}} \times \frac{1 \text{ h}}{3600 \text{ s}} \][/tex]

[tex]\[ \Delta p \approx 1.0032 \times 10^{-18} \text{ kg·m/s} \][/tex]

Now, calculate [tex]\( \Delta x \):[/tex]

[tex]\[ \Delta x \geq \frac{\hbar}{2 \Delta p} \][/tex]

[tex]\[ \Delta x \geq \frac{6.626 \times 10^{-34} \text{ J·s}}{2 \times 1.0032 \times 10^{-18} \text{ kg·m/s}} \][/tex]

[tex]\[ \Delta x \geq 3.31 \times 10^{-16} \text{ m} \][/tex]

Answer: Molality of solution is 0.89 mole/kg

Explanation:

Molality of a solution is defined as the number of moles of solute dissolved per kg of the solvent.

[tex]Molarity=\frac{n}{W_s}[/tex]

where,

n = moles of solute

[tex]W_s[/tex] = weight of solvent in kg

moles of nitrobenzene (solute) =[tex]\frac{\text {given mass}}{\text {Molar Mas}}=\frac{1.1}{123.06g/mol}=0.0089[/tex]

mass of napthalene (solvent )= 10.0 g = 0.0100 kg

Now put all the given values in the formula of molality, we get

[tex]Molality=\frac{0.0089}{0.0100kg}=0.89mole/kg[/tex]

Therefore, the molality of solution is 0.89 mole/kg

Answer: The partial pressure of carbon dioxide is 476.

Explanation:

We are given:

Moles of oxygen gas = 3.63 moles

Moles of nitrogen gas = 1.49 moles

Moles of carbon dioxide gas = 6.16 moles

Total number of moles = [3.63 + 1.49 + 6.16] = 11.28 moles

Mole fraction of a substance is given by:

[tex]\chi_A=\frac{n_A}{n_A+n_B}[/tex]

Mole fraction of carbon dioxide, [tex]\chi_{CO_2}=\frac{n_{CO_2}}{n_T}[/tex]

So, [tex]\chi_{CO_2}=\frac{6.16}{11.28}=0.546[/tex]

To calculate the partial pressure of carbon dioxide, we use the equation given by Raoult's law, which is:

[tex]p_{CO_2}=p_T\times \chi_{CO_2}[/tex]

where,

[tex]p_A[/tex] = partial pressure of carbon dioxide = ?

[tex]p_T[/tex] = total pressure = 871 mmHg

[tex]\chi_{CO_2}[/tex] = mole fraction of carbon dioxide = 0.546

Putting values in above equation, we get:

[tex]p_{CO_2}=871mmHg\times 0.546\\\\\chi_{CO_2}=475.6mmHg=476.mmHg[/tex]

Hence, the partial pressure of carbon dioxide is 476.

Answer: 13.5g of O2

Explanation:

2C2H5OH + 7O2 → 4CO2 + 6H2O

Molar Mass of C2H5OH = (12x2)+5+16+1= 46g/mol

Mass conc. Of C2H5OH =2x46= 92g

Molar Mass of O2 = 32g/mol

Mass conc. Of O2 = 7 x 32 = 224g

From the equation,

92g of C2H5OH required 224g O O2.

Therefore, 5.54g of C2H5OH will require = (5.54x224)/92 = 13.5g of O2

To burn 5.54 g of C2H5OH, 13.4 g of O2 is required.

To determine the grams of oxygen gas required to burn 5.54 g of C2H5OH, we first need to convert the given mass of C2H5OH to moles using its molar mass. The molar mass of C2H5OH is 46.07 g/mol. So, 5.54 g of C2H5OH is equal to 5.54 g / 46.07 g/mol = 0.12 mol of C2H5OH.

According to the balanced equation, the mole ratio between C2H5OH and O2 is 2:7. Therefore, for every 2 moles of C2H5OH, we require 7 moles of O2.

Using this mole ratio, we can calculate the moles of O2 required: 0.12 mol C2H5OH × (7 mol O2 / 2 mol C2H5OH) = 0.42 mol O2.

To convert moles of O2 to grams, we can use its molar mass, which is 32.00 g/mol. Therefore, 0.42 mol O2 × 32.00 g/mol = 13.4 g of O2.

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Explanation:

[tex]\Delta T_b=T_b-T[/tex]

[tex]\Delta T_b=K_b\times m[/tex]

[tex]Delta T_b=iK_b\times \frac{\text{Mass of solute}}{\text{Molar mass of solute}\times \text{Mass of solvent in Kg}}[/tex]

where,

[tex]\Delta T_f[/tex] =Elevation in boiling point

[tex]K_b[/tex] = boiling point constant of solvent

i =  van't Hoff factor

m = molality

As we can see that molality is directly proportional ti elevation in boiling point, so higher the molality of the solution at more high temperature it will boil.

1) 0.16 m [tex]Pb(CH_3COO)_2[/tex]

i = 3

[tex]\Delta T_b=3K_b\times 0.16 m=K_b\times 0.48 m[/tex]

Third highest boiling point

2) 0.17 m [tex]NiBr_2[/tex]

i = 3

[tex]\Delta T_b=3K_b\times 0.17 m=K_b\times 0.51 m[/tex]

Second highest boiling point  

3) [tex]8.8\times 10^{-2} m[/tex] of  [tex]Al_2(SO_4)_3[/tex]

i = 5

[tex]\Delta T_b=5\times K_b\times 8.8\times 10^{-2} m=K_b\times 0.44 m[/tex]

Lowest boiling point

4) 0.53 m Urea

i = 1

[tex]\Delta T_b=1\times K_b\times 0.53 m =K_b\times 0.53 m[/tex]

Highest boiling point

The boiling point of a solution depends on the concentration and nature of the solute. Electrolytes increase the boiling point, while nonelectrolytes do not. In this case, the solutions with Pb(CH3COO)2, NiBr2, and Al2(SO4)3 have higher boiling points than the solution with urea.

The boiling point of a solution is influenced by the concentration and nature of the solute. In this case, we are given four solutions with different concentrations and solutes. To determine the boiling point, we need to consider the number of particles the solute breaks into when it dissolves. Electrolytes like Pb(CH3COO)2, NiBr2, and Al2(SO4)3 break into ions and increase the boiling point while urea, a nonelectrolyte, does not break into ions and has a lower boiling point.

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Answer:

Approximately [tex]1.29 \times 10^3[/tex] grams.

Explanation:

Let [tex]x[/tex] represent the number of grams of aluminum iodide required to yield that 73.75 grams of aluminum.  

In most cases, the charge on each aluminum ion would be +3 while the charge on each iodide ion would be -1. For the charges to balance, there needs to be three iodide ions for every aluminum ion. Hence, the empirical formula for aluminum iodide would be [tex]\rm AlI_3[/tex].

How many moles of formula units in that [tex]x[/tex] grams of [tex]\rm AlI_3[/tex]? Start by calculating its formula mass [tex]M(\mathrm{AlI_3})[/tex]. Look up the relative atomic mass of aluminum and iodine on a modern periodic table:

[tex]M(\mathrm{AlI_3}) = 1\times 26.982 + 3\times 126.904 = 410.694\; \rm g \cdot mol^{-1}[/tex].

[tex]n(\mathrm{AlI_3}) = \displaystyle \frac{m}{M} = \frac{x}{410.694}\;\rm mol[/tex].

Since there's one aluminum ion in every formula unit,

[tex]n(\mathrm{Al}) = n(\mathrm{AlI_3}) = \displaystyle \frac{x}{410.694}\; \rm mol[/tex].

How many grams of aluminum would that be?

[tex]m(\mathrm{Al}) = n \cdot M = \displaystyle \frac{x}{410.694}\; \times 26.982 = \frac{26.982}{410.694}\, x\; \rm g[/tex].

However, since according to the question, the percentage yield (of aluminum) is only [tex]86.8\%[/tex]. Hence, the actual yield of aluminum would be:

[tex]\begin{aligned}&\text{Actual Yield} \\ &= \text{Percentage Yield} \times \text{Theoretical Yield} \\ &= 86.8\% \times \frac{26.982}{410.694}\, x \\ &= 0.868 \times \frac{26.982}{410.694}\, x \\ &\approx 0.0570263\, x\; \rm g\end{aligned}[/tex].

Given that the actual yield is 73.75 grams,

[tex]0.0570263\, x = 73.75[/tex].

[tex]\displaystyle x = \frac{73.75}{0.0570263} \approx 1.29 \times 10^3\; \rm g[/tex].

To yield 73.75 grams of aluminum with a percent yield of 86.8%, approximately 1113.33 grams of aluminum iodide would be required.

To determine the amount of aluminum iodide required to yield 73.75 grams of aluminum with a percent yield of 86.8%, we need to use stoichiometry and the concept of percent yield.

First, we need to determine the theoretical yield of aluminum iodide using the balanced chemical equation: 2 Al + 3 I2 → 2 AlI3

From the equation, we can see that 2 moles of Al react with 3 moles of I2 to produce 2 moles of AlI3. Therefore, the molar ratio between Al and AlI3 is 2:2.

To calculate the theoretical yield of AlI3, we need to convert the mass of Al to moles using the molar mass of Al. Then, we use the mole ratio to find the moles of AlI3, and finally, convert it back to grams using the molar mass of AlI3.

Using the molar mass of Al (26.98 g/mol), we find that the moles of Al is 73.75 g / 26.98 g/mol = 2.73 moles.

Since the molar ratio between Al and AlI3 is 2:2, the moles of AlI3 produced is also 2.73 moles.

Finally, we can calculate the mass of AlI3 using the molar mass of AlI3 (407.7 g/mol): 2.73 moles * 407.7 g/mol = 1113.33 g.

Therefore, approximately 1113.33 grams of aluminum iodide would be required to yield an actual amount of 73.75 grams of aluminum with a percent yield of 86.8%.

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Answer: 133.3g/mol

Explanation:

Mass = 12g

V = 2L

R = 0.0821 L atm/ mol K

P = 836mmHg = 836/760 = 1.1atm

T = 25°C = 25 + 273 = 298K

n =?

n = PV /RT = (1.1x2)/(0.0821x298)

n = 0.09

Molar Mass = Mass / n

Molar Mass = 12/0.09

Molar Mass = 133.3g/mol

To find the molecular weight of a gas, use the ideal gas law equation PV = nRT, and rearrange to solve for n. Substitute the given values into the equation and calculate the number of moles. Divide the given mass by the number of moles to find the molecular weight of the gas.

To calculate the molecular weight of a gas, we can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Rearranging the equation to solve for n, we get n = PV /RT.

We can substitute the given values: P = 836 mmHg, V = 2.00 L, R = 0.0821 L atm/ mol K, and T = 25.0°C + 273.15 = 298.15 K.

By plugging in these values, we can find the number of moles, n, and then calculate the molecular weight using the formula: molecular weight = mass / number of moles. Since the mass is given as 12.0 g, we divide it by n to find the molecular weight of the gas.

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Explanation:

Answer:

90g

Explanation:

We need to find the molar mass of C6H12O6. This is done below:

MM of C6H12O6 = (12x6) + (12x1) + (6x16) = 72 + 12 + 96 = 180g/mol

From the question, we obtained:

Volume = 1L

Molarity = 0.5M

Number of mole = Molarity x Volume

Number of mole = 0.5 x 1 = 0.5mol

Mass conc of C6H12O6 = number of mole x MM = 0.5 x 180 = 90g

To make 1 L of a 0.5 M solution of glucose, one would need 90.078 grams of glucose, based on the molecular weight calculation of C6H12O6.

To calculate how many grams of glucose (C6H12O6) are needed to make 1 L of a 0.5 M solution, you first need to calculate the molar mass of glucose. The molar mass can be found by adding up the atomic masses of all the atoms in one molecule of glucose. The atomic masses are approximately carbon (C) 12.01 g/mol, hydrogen (H) 1.008 g/mol, and oxygen (O) 16.00 g/mol. So, the molar mass of C6H12O6 is:

Next, you use the molarity equation which is:

Molarity (M) = moles of solute / liters of solution

For a 0.5 M solution, you require 0.5 moles of glucose per liter of solution. Using the molar mass calculated earlier, the mass of glucose needed is:

(0.5 moles) ×(180.156 g/mol) = 90.078 g

Therefore, you would need 90.078 g of glucose to make 1 L of a 0.5 M solution of glucose.