Calculate the pH of a solution prepared by dissolving 0.270 mol of formic acid (HCO₂H)and 0.260 mol of sodium formate (NaCO₂H)in water sufficient to yield 1.00 L of solution. The K_a of formic acid is 1.77 × 10^-4. A)2.099 B)10.264 C)3.736 D)2.307 E)3.952

Question

Quizplus · Accepted Answer

First, we need to find the concentration of formic acid and formate ion in the solution:
[HCOS1U1B12S1U1B0H] = 0.270 mol/1.00 L = 0.270 M
[NaCOS1U1B12S1U1B0H] = 0.260 mol/1.00 L = 0.260 M

Since sodium formate is a strong electrolyte, it will dissociate completely in water to form Na+ and formate ion. Therefore, the concentration of formate ion is equal to the concentration of sodium formate:
[COS1U1B12S1U1B0^-] = 0.260 M

Formic acid is a weak acid, so we can use the formula for the dissociation constant of a weak acid (Ka) to calculate the concentration of H+ ions in the solution:

Ka = [H+][COS1U1B12S1U1B0^-]/[HCOS1U1B12S1U1B0H]

We know the value of Ka (1.77 × 10S1U1P1-4S1S1P0) and the concentrations of formic acid and formate ion, so we can rearrange the equation to solve for [H+]:

[H+] = sqrt(Ka*[HCOS1U1B12S1U1B0H]/[COS1U1B12S1U1B0^-])

[H+] = sqrt((1.77 × 10S1U1P1-4S1S1P0)*(0.270)/(0.260))

[H+] = 1.88 × 10S1U1P-4S1S1P0

Finally, we can use the equation for pH to find the pH of the solution:

pH = -log[H+]

pH = -log(1.88 × 10S1U1P-4S1S1P0)

pH = 3.736

Therefore, the pH of the solution is 3.736, which corresponds to choice C.

Calculate the PH of a Solution Prepared by Dissolving 0