A 0.150 M solution of nitrous acid (HNO2) is made. Ka = 4.5 x 10-4
1. Show the equilibrium which occurs when this acid is dissolved in water.
2. What is the pH of the solution? Show all work clearly.
3. 100.0 mL of the solution is titrated against 0.150 M NaOH. What is the pH at the equivalence point?
4. What is true about the pH and pKa, and the [acid] and [conjugate base] at the half-equivalence point?
..........HNO2 + H2O ==> H3O^+ + NO2^-
initial...0.150M..........0........0
change.....-x.............x........x
equil...0.150-x...........x.........x
Ka = (H3O^+)(NO2^-)/(HNO2)
Substitute from the ICE chart and solve for x = (H3O^+). Then pH = -log(H3O^+)
3.
Calculate volume NaOH needed to arrive at the equivalence point and from that the the concn of the salt at that point. The pH at the equivalence point is determined by the hydrolysis of the salt. I will call the concn of the salt C.
.........NO2^- + HOH ==> HNO2 + OH^-
initial...c................0.....0
change...-x...............x.......x
equil....c-x...............x......x
Kb for NO2^- = (Kw/Ka for HNO2) = (HNO2)(OH^-)/(HNO2)
Substitute and solve for x = (OH^-), then convert to pH.
At the half way point pH = pKa.
1. To show the equilibrium which occurs when nitrous acid (HNO2) is dissolved in water, we need to write the chemical equation:
HNO2 + H2O ⇌ H3O+ + NO2-
In this equation, HNO2 donates a proton (H+) to water (H2O) forming hydronium ion (H3O+), and the resulting conjugate base is nitrite ion (NO2-).
2. To find the pH of the solution, we can use the expression for the acid dissociation constant (Ka) and the initial concentration of the acid (HNO2).
The Ka expression for nitrous acid is:
Ka = [H3O+][NO2-] / [HNO2]
Since the initial concentration of nitrous acid is given as 0.150 M, we can assume that the concentration of H3O+ is initially 0. To simplify the calculation, we can also assume that the concentration of NO2- is negligible compared to HNO2 at the beginning.
Ka = [H3O+][0] / [0.150]
Now, we can solve for the concentration of H3O+ (which represents the initial hydronium ion concentration).
Ka = [H3O+]^2 / [0.150]
[H3O+]^2 = Ka * [HNO2]
[H3O+]^2 = (4.5 x 10^-4) * (0.150)
[H3O+]^2 = 6.75 x 10^-5
[H3O+] = √(6.75 x 10^-5)
[H3O+] ≈ 0.0082 M
Since pH is defined as the negative logarithm of the hydronium ion concentration, we can find the pH:
pH = -log([H3O+])
pH = -log(0.0082)
pH ≈ 2.08
Therefore, the pH of the solution is approximately 2.08.
3. At the equivalence point, the moles of acid (HNO2) are equal to the moles of base (NaOH) added. This means that all of the nitrous acid is neutralized and converted to its conjugate base (NO2-).
Since sodium hydroxide (NaOH) is a strong base, it dissociates completely in water to form hydroxide ions (OH-) and sodium ions (Na+):
NaOH → Na+ + OH-
The hydroxide ions react with the nitrous acid (HNO2) to form water (H2O) and the conjugate base (NO2-):
OH- + HNO2 → H2O + NO2-
At the equivalence point, since all the nitrous acid is neutralized, we only have the conjugate base (NO2-) left in solution.
To find the pH at the equivalence point, we need to calculate the pOH using the concentration of the conjugate base and then convert it back to pH.
Since the concentration of nitrous acid is not given in the question, we assume it is completely neutralized. Therefore, we can use the concentration of sodium hydroxide (0.150 M) to find the pOH.
pOH = -log([OH-])
pOH = -log(0.150)
pOH ≈ 0.82
To find the pH at the equivalence point, we can use the equation:
pH + pOH = 14
pH = 14 - pOH
pH ≈ 14 - 0.82
pH ≈ 13.18
Therefore, the pH at the equivalence point is approximately 13.18.
4. At the half-equivalence point, half of the nitrous acid is neutralized with the same number of moles of sodium hydroxide. This means that the concentration of nitrous acid is equal to the concentration of its conjugate base (NO2-).
At the half-equivalence point, the pH is equal to the pKa of the acid. The pKa is defined as the negative logarithm of the acid dissociation constant (Ka).
Therefore, the pH at the half-equivalence point is equal to the pKa of nitrous acid, and the concentration of the acid (HNO2) is equal to the concentration of its conjugate base (NO2-).