A buffer is prepared by adding 100 mL of 0.50 M sodium hydroxide to 100 mL of 0.75 M propanoic acid. Is this a buffer solution, and if so, what is its pH? A)It is a buffer, pH pK _a of propanoic acid. B)It is a buffer, pH

Question

A buffer is prepared by adding 100 mL of 0.50 M sodium hydroxide to 100 mL of 0.75 M propanoic acid. Is this a buffer solution, and if so, what is its pH? A)It is a buffer, pH > pK _a of propanoic acid. B)It is a buffer, pH < pK _a of propanoic acid. C)It is a buffer, pH = pK _a of propanoic acid. D)It is a buffer, pH = pK _b of sodium propanoate. E)Since sodium hydroxide is a strong base, this is not a buffer.

Quizplus · Accepted Answer

To determine if this is a buffer solution, we need to calculate the pH and compare it to the pKa of propanoic acid. 
The balanced equation for the reaction is:
CH3CH2COOH + NaOH --> CH3CH2COONa + H2O

To calculate the moles of each species present, we use the formula n = c x V.
n(NaOH) = 0.50 mol/L x 0.10 L = 0.05 mol
n(propanoic acid) = 0.75 mol/L x 0.10 L = 0.075 mol

Since NaOH completely dissociates in solution, we have 0.05 mol of OH- ions. 
These will react with the propanoic acid to form the conjugate base, sodium propanoate, and water:

OH- + CH3CH2COOH --> CH3CH2COO- + H2O

The amount of propanoic acid that reacts with the OH- ions is determined by the amount of sodium propanoate that is formed:

n(NaCH3CH2COO) = n(NaOH) = 0.05 mol

The amount of propanoic acid remaining is therefore:

n(CH3CH2COOH) = 0.075 - 0.05 = 0.025 mol

To calculate the concentrations of the conjugate acid and base, we divide the moles by the total volume of the solution (200 mL, or 0.2 L):

[CH3CH2COOH] = 0.025 mol / 0.2 L = 0.125 M
[CH3CH2COO-] = 0.05 mol / 0.2 L = 0.25 M

To determine the pH of the buffer, we use the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

The pKa of propanoic acid is 4.87.

pH = 4.87 + log(0.25/0.125) 
pH = 4.87 + 0.30 
pH = 5.17

Since the pH is greater than the pKa, this is a buffer solution. Therefore, choice A is correct.

A Buffer Is Prepared by Adding 100 ML of 0