Answer:
Explanation:
Molarity of acid(volume of acid)(# of H ions)= molarity of base(volume of base)(# of OH ions)
M(v)(#)=M(v)(#)
sulfuric acid sodium hydroxide
H2SO4 NaOH
(3)(11.6)(2)=M(25)(1)
M=2.784
The molarity of the NaOH solution is 2.784 M
We'll begin by writing the balanced equation for the reaction.
2NaOH + H₂SO₄ —> Na₂SO₄ + 2H₂OFrom the balanced equation above,
The mole ratio of the acid, H₂SO₄ ([tex]n_{a}[/tex]) = 1
The mole ratio of the base, NaOH ([tex]n_{b}[/tex]) = 2
From the question given above, the following data were obtained:
Volume of acid, H₂SO₄ ([tex]V_{a}[/tex]) = 11.6 mL
Molarity of acid, H₂SO₄ ([tex]M_{a}[/tex]) = 3 M
Volume of base, NaOH ([tex]V_{b}[/tex]) = 25 mL
Molarity of base, ([tex]M_{b}[/tex]) =?[tex]\frac{M_{a} V_{a}}{M_{b} V_{b}} = \frac{n_{a}}{n_{a}}\\\\ \frac{3 (11.6)}{M_{b} (25)} = \frac{1}{2}\\\\[/tex]
Cross multiply[tex]M_{b}[/tex] × 25 × 1 = 3 × 11.6 × 2
[tex]M_{b}[/tex] × 25 = 69.6
Divide both side by 25[tex]M_{b} = \frac{69.6}{25}\\ M_{b} = 2.784 M[/tex]
Therefore, the molarity of the NaOH solution is 2.784 M
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Where are the products in a chemical equation located
A On the left side of the snow in the equation
. On the night wide of the arrow in the equation
C. Between the reactants of the chemical equation
. At the beginning of the chemical equation
O
O
Answer:
the answer is B
Explanation:
reactants are on the left because they are the ones reacting. products are on the right because they are the final products.
Is burning of wood a reversible or irreversible change
Answer:
can you reverse the ashes back into wood? If you can't then it is irreversible
Describe the redox reaction. Check all that apply 2AI(s) + 3ZnCI2(g) → 3Zn(s) + 2AICI3(aq).
Aluminum atoms transfer electrons to chlorine atoms.
Zinc is reduced.
Zinc is the reducing agent.
The oxidation number of chlorine does not change.
Aluminum is oxidized.
Answer:
Zinc is reduced.
The oxidation number of chlorine does not change.
Aluminum is oxidized.
Explanation:
For the reaction:2AI(s) + 3ZnCI₂(g) → 3Zn(s) + 2AICI₃(aq).
For the elements in the reactants side:
Al has (0) oxidation state and converted to (+3) oxidation state in the products (AlCl₃), which means Al is oxidized and it is the reducing agent.
So, we can check that: Aluminum is oxidized.
Zn has the oxidation state (+2) in the reactants side (ZnCl₂) and converted to (0) in the products side (Zn), which means that Zn is reduced and it is the oxidizing agent.
So, we can check that: Zinc is reduced.
and can not check: Zinc is the reducing agent.
The oxidation state of Cl does not change, it is the same in both sides (-1).
So, we can check: The oxidation number of chlorine does not change.
and can not check: Aluminum atoms transfer electrons to chlorine atoms.
So, the choices will be:
Zinc is reduced.
The oxidation number of chlorine does not change.
Aluminum is oxidized.
Answer: B, D,E
Explanation:
0.00781 g = kg
helppppp
Answer: The answer is: " 7.81 kg " .
___________________________________________________
Explanation:
___________________________________________________
Note the exact conversion: 1000 g = 1 kg ;
0.00781 g = ? kg :
So: To convert "0.0781 g" ; to "units in kg" ;
→ we multiply the value: 0.00781 g ; by "1000" ;
So: Given: " 0.00781 g " ;
→ we move the decimal point "3 (three) spaces forward" ;
to get: " 7.81 kg " .
___________________________________________________
Hope this helps!
Wishing you the best in your academic pursuits
— and within the "Brainly" community!
___________________________________________________
Answer:
0.00000781kg
Explanation:
which of the following is described by the equation H2O(s)+ heat=H2O(I)
A Freezing
Melting
Condensing
Evaporating
Answer: Melting
Explanation: Just confirming the other answer
This equation described is of Melting.
What is melting?Melting is the change of a solid into a liquid when heat is applied to the substance.How solid changes to liquid in heating? Application of heat to the molecules of a solid , speed up the motion and molecules overcomes the attractions and move past each other as a liquid.
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Which of the following lists the atmospheric layers in the correct order beginning at the Earth's surface?
Answer:Troposphere, Stratosphere, Mesosphere and Thermosphere
Explanation:
Which of the following is an example of point-source pollution? A. Salt from roads B. Water from a sewage treatment plant C. Fertilizer from agricultural runoff D. Acid from abandoned mines
Answer:
Acid from abandoned mines- D.
Answer:
Water from a sewage treatment plant
Explanation:
Water from a sewage treatment plant is an example of point-source pollution.
“Gasoline boils at a relatively low temperature (about 150°C). The kerosene is removed at around 200°C, followed by diesel oil at 300°C and fuel oil at around 370°C.”
What topic is the teacher most likely talking about?
Answer:
Explanation:
Quick Answer: Likely fractional distillation.
The distillation taking place has heat that is not uniformly distributed. Hot air rises, so the temperature at the top is greated than at the bottom. When petroleum is distilled various organics come off at various temperatures and at different levels of distillery apparatus.
plese HELP I AM NEW
On the basis of Bohr's model, the radius of the 3rd orbit
is -
(A) Equal to the radius of first orbit
(B) Three times the radius of first orbit
(C) Five times the radius of first orbit
(D) Nine time the radius of first orbit
Answer:
[tex]\boxed{\text{(D) Nine times the radius of the first orbit}}[/tex]
Explanation:
On the basis of Bohr's model, the radius of the nth orbit is
r = a₀n²
where a₀ is a constant called the Bohr radius.
r₃\r₁ = (a₀ × 3)²/(a₀ × 1)² = 9/1 = 9
The radius of the third Bohr orbit is nine times the radius of the first orbit.
Answer:
The correct answer is option D.
Explanation:
Formula used for the radius of the [tex]n^{th}[/tex] orbit will be,
[tex]r_n=\frac{n^2\times 52.9}{Z}[/tex] (in pm)
where,
[tex]r_n[/tex] = radius of [tex]n^{th}[/tex] orbit
n = number of orbit
Z = atomic number
Radius of the first orbit, n = 1
[tex]r_1=\frac{1^2\times 52.9}{Z}=\frac{1\times 52.9}{Z}[/tex]..[1]
Radius of the third orbit, n = 3
[tex]r_3=\frac{3^2\times 52.9}{Z}=\frac{9\times 52.9}{Z}[/tex]..[2]
[1] ÷ [2]
[tex]\frac{r_1}{r_3}=\frac{\frac{1\times 52.9}{Z}}{\frac{9\times 52.9}{Z}}[/tex]
[tex]r_1\times 9=r_3[/tex]
The radius of the 3rd orbit is nine times the radius of first orbit.
Which statement correctly identifies the nuclide that is most likely to be unstable and describes why?
a) Carbon-14 (14C) is likely an unstable nuclide because it has 8 neutrons and 6 protons, and the ideal neutron-to-proton ratio is 1:5.
b) Uranium-238 (238U) is likely an unstable nuclide because it has a neutron-to-proton ratio that is 1.6:1 and the ideal neutron-to-proton ratio is 1:1.
c) Carbon-14 (14C) is likely an unstable nuclide because it has 8 neutrons and 6 protons, and the ideal neutron-to-proton ratio is 1:2.
d) Uranium-238 (238U) is likely an unstable nuclide because it has a neutron-to-proton ratio that is 1.6:1 and the ideal neutron-to-proton ratio is 1:2.
What happens when an atom of sulfur combines with two atoms of chlorine to produce SCI2?
A.
Each chlorine atom shares a pair of electrons with the sulfur atom.
B.
An electron is transferred from each chlorine atom to the sulfur atom.
C.
An electron is transferred from the sulfur atom to each chlorine atom.
D.
Each chlorine atom shares all its valence electrons with the sulfur atom.
Answer:
A.) Each chlorine atom shares a pair of electrons with the sulfur atom.
There are two types of chemical compound one is covalent compound and another is ionic compound in chemistry. In ionic bonds, electrons are completely transferred. The correct option is option A.
What is chemical Compound?Chemical Compound is a combination of molecule, Molecule forms by combination of element and element forms by combination of atoms in fixed proportion.
Covalent compounds are formed by covalent bond and ionic compounds are formed by ionic bond. The melting and boiling points are higher in ionic compounds.
Covalent bond is formed by sharing of electron and ionic bond are formed by complete transfer of electron. Ionic bonds are stronger than covalent bonds. SCI[tex]_2[/tex] is a covalent compound. During formation of SCI[tex]_2[/tex], each chlorine atom shares a pair of electrons with the sulfur atom.
Therefore, the correct option is option A.
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If a simple machine aduces the strength of a force, what must be increased?
the speed of the input force
the work the simple machine performs
the size of the simple machine
the distance over which the force is applied
Answer:
the work the simple machine performs (second choice)
When the volume and number of particles of a gas are constant which of the following is also constant
It is the Avogadro's law which explains the relationship between the number of moles and the volume. When the volume and the number of moles are constant then the pressure and temperature are constant.
What is Avogadro's law?The law states that equal volumes of all gases under the similar conditions of temperature and pressure contains equal number of molecules. The law can be mathematically expressed as:
V ∝ n
Here 'V' is the volume and 'n' is the number of moles.
It follows that the volume of a gas is directly proportional to the number of molecules. But the number of molecules (N) of a gas is directly proportional to the number of moles (n).
Thus when the volume and number of particles of a gas are constant then the pressure and temperature are also found to be constant.
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Which of the following elements would you expect to have the lowest ionization energy value? Fluorine, lithium, neon, nitrogen
Answer:
Lithium (Li)
Explanation:
Lithium had the lowest ionization energy value because it has a low effective nuclear charge and a large radius
Answer:
lithium
Explanation:
State Avogadro's Hypothesis.
Answer: Avogadro's Hypothesis simply states that all gases of equal volume have the same number of molecules.
Explanation: Avogadro's Hypothesis is an experimental gas law and it serves as a specific case of the ideal gas law. Mathematically,
Volume (V) is proportional to the Number of mole (n) of the gas
V/n = K
Where K is the constant of proportionality.
Avogadro's hypothesis states that equal volumes of gases contain the same number of particles. It is an important concept in the study of gases.
Explanation:Avogadro's hypothesis states that equal volumes of gases, at the same temperature and pressure, contain the same number of particles. This hypothesis helps explain the concept of molar volume and is a fundamental principle in the study of gases. For example, 1 mole of any gas occupies the same volume as 1 mole of any other gas at the same temperature and pressure.
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A solution is made by dissolving 19.5 grams of glucose (C6H12O6) in 0.245 kilograms of water. If the molal freezing point constant for water (Kf) is -1.86 °C/m, what is the resulting Δtf of the solution? Show all he steps taken to solve this problem.
Will make brainliest!!
20 points!!
Answer:
- 0.8217°C.
Explanation:
We can solve this problem using the relation:ΔTf = Kf.m,
ΔTf is the depression in the freezing point.
Kf is the molal freezing point constant for water (Kf = -1.86 °C/m).
m is the molality of glucose.
We need to calculate the molality:Molality (m) is the no. of moles of solute in 1.0 kg of solvent.
∴ m = (mass/molar mass) of glucose/(mass of water (kg))
∴ m = (19.5 g/180.156 g/mol)/(0.245 kg) = 0.4418 m.
∴ ΔTf = Kf.m = (-1.86 °C/m)(0.4418 m) = - 0.8217°C.
Jason combines the two intermediate steps shown.
Na(g)+O2(g) ->2NO(g)
2NO(g)+O2(g) 2NO2(g)
Which best describes what Jason should do with the oxygen molecules?
Place two of them as products.
Place two of them as reactants.
Cancel them out because there is one in each equation.
Double them because there is one in each equation.
Answer:
Place two of them as reactants.
Explanation:
We have the two steps of reactions:1) N₂(g ) + O₂(g) → 2NO(g).
2) 2NO(g )+ O₂(g) → 2NO₂(g).
Adding the two equation with cancelling the intermediate (NO), we get:
N₂(g ) + 2O₂(g) → 2NO₂(g).
NO is cancelled out because there is one in each equation in the products side in eq. 1 and in oriduct side in eq. 2.
So, we place two of oxygen as reactants.
Answer:
Place two of them as reactants
Explanation:
Blood serum is typically about 0.0044 M in K+ (aq). Calculate the mass of the potassium ions in 4,785. mL of blood serum. The molar mass of potassium is 39.10 g/mol
Answer:
0.823 g.
Explanation:
Molarity (M) is defined as the no. of moles of solute dissolved in a 1.0 L of the solution.M = (no. of moles of K⁺)/(Volume of the solution (L).
∵ no. of moles of K⁺ = (mass/molar mass) of K⁺.
∴ M = (mass/molar mass) of K⁺/(Volume of the solution (L).
M = 0.0044 M.
Volume of the solution = 4785.0 mL = 4.785 L.
mass of K⁺ = ??? g.
molar mass of K⁺ = 39.01 g/mol.
∴ mass of K⁺ = (M)((molar mass of K⁺)(volume of the solution (L)) = (0.0044 M)(39.10 g/mol)(4.785 L) = 0.823 g.
When the pressure that a gas exerts
on a sealed container changes from
22.5 psi to_ psi, the
temperature changes from 110°C to
65.9°C.
The answer is:
When the pressure that a gas exerts on a sealed container changes from
22.5 psi to 19.86 psi, the temperature changes from 110°C to
65.9°C.
Why?To calculate which is the last pressure, we need to use Gay-Lussac's law.
The Gay-Lussac's Law states that when the volume is kept constant, the temperature (absolute temperature) and the pressure are proportional.
The Gay-Lussac's equation states that:
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]
We are given the following information:
We need to remember that since the temperatures are given in Celsius degrees, we need to convert it to Kelvin (absolute temperature) before use the equation, so:
[tex]P_1=22.5Psi\\T_1=110\°C=110\°C+273.15=383.15K\\T_1=65.9\°C=65\°C+273.15=338.15K[/tex]
Now, calculating we have:
[tex]\frac{P_1}{T_1}*(T_2)=P_2\\\\P_2=\frac{P_1}{T_1}*(T_2)=\frac{22.5Psi}{383.15}*338.15=19.86Psi[/tex]
Hence, the final pressure is equal to 19.86 Psi.
Have a nice day!
Answer:
The final pressure at 65.9°C is 19.91 psi.
Explanation:
To calculate the final pressure of the system, we use the equation given by Gay-Lussac Law.
This law states that pressure of the gas is directly proportional to the temperature of the gas at constant pressure.
Mathematically,
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex] (at constant Volume)
where,
[tex]P_1\text{ and }T_1[/tex] are the initial pressure and temperature of the gas.
[tex]P_2\text{ and }T_2[/tex] are the final pressure and temperature of the gas.
We are given:
[tex]P_1=22.5 psi\\T_1=110^oC=383.15 K\\P_2=?\\T_2=65.9^oC=339.05 K[/tex]
Putting values in above equation, we get:
[tex]\frac{22.5 psi}{383.15 K}=\frac{p_2}{339.05 K}[/tex]
[tex]P_2=\frac{22.5 psi}{383.15 K}\times 339.05 K=19.91 psi[/tex]
The final pressure at 65.9°C is 19.91 psi.
Water striders are insects that have the ability to walk across the surface of water. Which properties of water allow the water strider to do this? Choose 2 answers: Choose 2 answers: (Choice A) A Surface tension (Choice B) B Adhesion (Choice C) C Specific heat (Choice D) D Capillary action
The properties of water that enables the water striders to walk across the surface of water is surface tension and adhesion.
Surface tension is a force that acts on the surface of water that makes it behave as if it is a stretched elastic skin. The ability of water molecules to stick to other surfaces is called adhesion.
As a result of surface tension and adhesion, insects such as water striders are able to walk across the surface of water.
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Express the following number in scientific notation.
0.026890 =
To express 0.026890 in scientific notation, it is written as 2.6890 x [tex]10^{-2}[/tex].
Express the following number in scientific notation:
0.026890 = 2.6890 x [tex]10^{-2}[/tex]
Scientific notation is a way to represent very large or very small numbers more concisely. It is written as a number between 1 and 10 multiplied by a power of 10.
How do you measure density
Answer:
d = m / v
Explanation:
This is the formula for density. d stands for density. m stands for mass. lastly, v stands for volume. just divide the mass by the volume and boom, you've got the density of an object ^-^
why is radioactive dating important when approximating the age of earth?
Answer:
So, we rely on radiometric dating to calculate their ages. Radiometric dating, or radioactive dating as it is sometimes called, is a method used to date rocks and other objects based on the known decay rate of radioactive isotopes.
Explanation:
radiometric dating is a very accurate way to date the Earth.We know it is accurate because radiometric dating is based on the radioactive decay of unstable isotopes. When an unstable Uranium (U) isotope decays, it turns into an isotope of the element Lead (Pb).
Answer:
The radioactive dating method is one of the efficiently used methods in order to calculate the age of the rocks, meteorites, fossils and various other objects, depending upon the rate at which radioactive isotopes decay. In this method, an unstable element changes into a stable one, releasing some amount of radiation and losing a certain amount of energy.
This is efficient in determining the age of the earth. The earth is comprised of rocks that are present from the time of its formation. These rocks can be dated using this method and the approximate age of the rock is evaluated.
The Uranium-Lead dating (²³⁸U-²⁰⁶Pb) method was used to date the smaller zircon crystals of Australia that are about 4.4 billion years old. The half-life of U-238 is approximately 4.5 billion years, which shows that these are one of the oldest rocks on earth and helps in understanding how old the earth is.
Half-life is defined as the time required by a radioactive isotope to decay half of its atoms.
So the radioactive dating method is one of the common method gives the approximate age of the earth.
How is an endothermic reaction identified
Answer:
An endothermic reaction is identified by noting the drop in temperature in the system.
Explanation:
An endothermic reaction occurs by absorbing heat energy from the environment( apparatus and solution). Once the energy in the surrounding reduces the temperature drops. The energy absorbed is used to form new bonds. The energy absorbed is directly proportional to the temperature drop.
Answer:
An endothermic reaction absorbs heat from its surroundings.
Explanation:
An example is the reaction of acetic acid with baking soda.
Three ways to tell if a reaction is endothermic:
Do the experiment. The system cools down, and you can use a thermometer or your hand to tell that the flask becomes colder .Heat will appear as a reactant in the chemical equation:CH₃COOH + NaHCO₃ + heat ⟶ CH₃COONa + H₂O + CO₂ The sign of ΔH is positive. N₂ + 2O₂ ⟶ 2NO₂ ; ΔH = +33.1 kJ·mol⁻¹The molar volume of a gas at STP, in liters, is
In which of the following is concentration expressed in percent by volume?
10% (v)
10% (m/m)
10% (m/v)
10% (v/v)
Answer:
Concentration expressed in percent by volume by volume is 10%(v/v).
Explanation:
w/w % or m/m% : The percentage mass or fraction of mass of the of solute present in total mass of the solution.[tex]w/w\%=\frac{\text{Mass of solute}}{\text{Mass of solution}}\times 100[/tex]
w/v % or m/v: The percentage of mass of the of solute present in total volume of the solution.[tex]w/v\%=\frac{\text{Mass of solute}}{\text{Volume of solution}}\times 100[/tex]
v/v % : The percentage volume of the of solute present in total volumeof the solution.[tex]v/v\%=\frac{\text{Volume of solute}}{\text{Volume of solution}}\times 100[/tex]
Concentration expressed in percent by volume by volume is 10%(v/v).
The concentration expressed in percent by volume is 10% (v/v). This denotes that 10% of the total volume of the solution is made up of a particular solute.
Explanation:Concentration expressed in percent by volume is represented as 10% (v/v). This means that the percentage is derived from the ratio of the volume of the solute to the volume of the solution, and then multiplied by 100 to get the percentage. For instance, if you have a solution with 10ml of ethanol mixed with 90ml of water, the volume ratio of ethanol to the total solution is 10ml/100ml=0.1, and when multiplied by 100 we get a 10% (v/v) ethanol solution. It's reflected as 10% of the total volume of the solution is comprising of the solute (ethanol).
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How much heat, in joules and in calories, is required to heat a 28.4-g (1-oz) ice cube from −23.0 °C to −1.0 °C?
a. The quantity of heat in Joules is equal to 1,305.832 Joules.
b. The quantity of heat in Calories is equal to 312.10 Cal.
Given the following data:
Mass of ice cube = 28.4 gramsInitial temperature = -23.0°CFinal temperature = -1.0°CScientific data:
Specific heat capacity of ice = 2.09 J/g°CTo determine the quantity of heat in Joules:
Mathematically, quantity of heat is given by the formula;
[tex]Q=mc\theta[/tex]
Where:
Q represents the quantity of heat.m represents the mass of an object.c represents the specific heat capacity.∅ represents the change in temperature.Substituting the given parameters into the formula, we have;
[tex]Q = 28.4 \times 2.09 \times (-1.0 -[-23.0])\\\\Q=59.356 \times (-1.0+23.0)\\\\Q=59.356 \times22[/tex]
Quantity of heat, Q = 1,305.832 Joules.
In Calories:
[tex]Calories =\frac{1305.832}{4.184}[/tex]
Calories = 312.10 Cal.
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The pressure on 7.0 L of gas is increased from 15 psi to 1420 torr, at constant
temperature. What is the new volume of the gas?
Answer:
3.85L
Explanation:
Given parameters:
Initial pressure P₁ = 15psi (1psi = 52mmHg)
converting to mmHg gives (15x52)mmHg = 780mmHg
Initial volume V₁ = 7.0L
Final pressure P₂ = 1420torr= 1420mmHg
Unknown:
Final volume V₂ = ?
Condition of the process: Constant temperature
Solution
To solve this problem, we simply apply Boyle's law. Boyle's law states that "The volume of a given mass of gas varies inversely as the pressure changes, if the temperature is constant".
It is mathematically expressed as ;
P₁V₁ = P₂V₂
The unknown here is V₂ and we simply express it as the subject of the formula:
V₂ = [tex]\frac{P_{1} V_{1} }{P_{2} }[/tex]
V₂ = [tex]\frac{780 x 7 }{1420}[/tex]
V₂ = [tex]\frac{5460}{1420}[/tex] = 3.85L
Once formed how are coordinates covalent bonds different for other covalent bonds?
Answer:
Explanation:
Coordinate covalent bonds differs from other types of covalent bonds in that the two atoms bonds in such a way that one member of the bonding pair supplies both electrons to be shared. In normal covalent bonds, both atoms supplies the electrons to be shared.
This type of bond is used to join two covalent compounds together. They can also be used in joining protons to neutral covalent molecules together.
Final answer:
Once established, coordinate covalent bonds are indistinguishable in strength and function from other covalent bonds.
Explanation:
The question asks about the difference between a coordinate covalent bond and other covalent bonds once they are formed. A coordinate covalent bond is a type of covalent bond where a single atom provides a pair of
electrons for the bond, while a regular covalent bond involves each atom contributing one electron to the shared pair. A classic example of a coordinate covalent bond is found in the carbon monoxide molecule (CO), where one of the three bonds between carbon and oxygen is a coordinate covalent bond because oxygen donates both electrons for that bond.
However, once formed, a coordinate covalent bond is just as strong and behaves in the same way as any other covalent bond.
Atoms typically form a characteristic number of covalent bonds that can include double bonds or triple bonds, as depicted in Lewis electron dot diagrams. Whether a bond is a coordinate covalent bond or not does not affect the eventual strength or final properties of the bond.
The following questions A24 - A26 relate to 100 ml of 0.0150 M solution of benzoic acid
(C6H3COOH). Ka(C6H3COOH) = 6.4 x 10^-5.
What is the pH of the solution after the addition of 1 x 10^-3 moles of NaOH? You may assume no volume change to the solution upon addition of the NaOH.
Answer:
PH of the weak acid: approximately 2.513.
PH of the buffer solution: approximately 4.495.
Explanation:
The Ka value of benzoic acid is much smaller than 1. Benzoic acid will dissociate but only partially when dissolved in water. Construct a RICE table for this process. Let the equilibrium of [tex]\rm H^{+}[/tex] be [tex]x\; \rm mol\cdot L^{-1}[/tex]. Note that [tex]x \ge 0[/tex].
[tex]\displaystyle \begin{array}{c|ccccc}\textbf{R}&\mathrm{C_6H_5COOH} & \rightleftharpoons & \mathrm{C_6H_5COO^{-}} & + &\mathrm{H^{+}}\\\textbf{I} & 0.015 & & 0 & & 0\\\textbf{C} & -x & & +x & & +x\\\textbf{E} & 0.015-x & & x & & x\end{array}[/tex]
[tex]\displaystyle \frac{[\mathrm{C_6H_5COO^{-}}]\cdot [\mathrm{H^{+}}]}{[\mathrm{C_6H_5COOH}]} = \mathrm{pK}_{a}[/tex].
[tex]\displaystyle \frac{x^{2}}{0.015 - x} = 6.4\times 10^{-5}[/tex].
Solve this quadratic equation for [tex]x[/tex]:
[tex]x^{2}+ 6.4\times 10^{-5}\;x - 6.4\times 10^{-5}\times 0.150 = 0[/tex].
[tex]\displaystyle x = \frac{-6.4\times 10^{-5} \pm \sqrt{(6.4\times 10^{-5})^{2} - 4\times (- 6.4\times 10^{-5}\times 0.150)}}{2}[/tex].
Take only the non-negative root. [tex]x \approx 0.00306655[/tex].
[tex]\rm [H^{+}] = 0.00306655\; mol\cdot L^{-1}[/tex].
[tex]\displaystyle \mathrm{pH} = -\log_{10}{[\mathrm{H^{+}}]} = 2.513[/tex].
Each benzoic acid contains only one carboxyl group [tex]\mathrm{-COOH}[/tex]. Benzoic acid is thus a monoprotic acid. Each mole of the acid will react with only one mole of [tex]\rm NaOH[/tex]. The 100 mL solution initially contains [tex]1.50\times 10^{-3}[/tex] moles of benzoic acid. The [tex]1\times 10^{-3}[/tex] moles of [tex]\rm NaOH[/tex] will neutralize only part of the acid. The solution will eventually contain [tex]1\times 10^{-3}[/tex] moles of [tex]\mathrm{C_6H_5COO^{-}}[/tex] (from the salt [tex]\mathrm{C_6H_5COONa}[/tex]) and [tex]0.50\times 10^{-3}[/tex] moles of [tex]\mathrm{C_6H_3COOH}[/tex].
Both the acid [tex]\mathrm{C_6H_5COOH}[/tex] and the conjugate base of the acid [tex]\mathrm{C_6H_5COO^{-}}[/tex] exist in large amounts in the solution. Apply the Henderson-Hasselbalch equation for weak acid buffers to find the pH of this buffer solution.
[tex]\mathrm{pK}_{a} = -\log_{10}{\mathrm{K}_{a}} \approx 4.19382[/tex] for benzoic acid.
[tex]\begin{aligned}\mathrm{pH} &= \mathrm{pK}_{a} + \log{\frac{{[\text{Conjugate Base}]}}{[\text{Weak Acid}]}} \\ &= \mathrm{pK}_{a} + \log{\frac{{[\mathrm{C_6H_5COO^{-}}]}}{[\mathrm{C_6H_5COOH}]}}\\ &= 4.19382 + \log{\frac{0.01}{0.005}}\\ &\approx 4.495 \end{aligned}[/tex].