a solution contain 0.50M propionic acid and 0.20M sodium propionate calculate ph? ka=1.3 × 10^-3
To calculate the pH of a solution containing propionic acid and sodium propionate, we need to consider the dissociation of the acid and the hydrolysis of the salt. Here's the step-by-step process to find the pH:
1. Write the dissociation equation of propionic acid (CH3CH2COOH):
CH3CH2COOH ⇌ CH3CH2COO- + H+
2. Since the acid dissociates partially, we need to determine the concentrations of the acid and its conjugate base. The concentration of propionic acid is given as 0.50 M, and the concentration of sodium propionate can be calculated by multiplying the concentration of propionic acid (0.50 M) with the ratio of dissociation (alpha):
[CH3CH2COONa] = [propionic acid] × alpha
Alpha is the degree of dissociation, assuming it is negligible because the sodium salt is a strong electrolyte, its value is 1.
[CH3CH2COONa] = 0.50 M × 1 = 0.50 M
3. Next, we calculate the concentration of hydronium ions (H+) by using the initial concentration of acid and its degree of dissociation.
[H+] = [acid] × alpha
[H+] = 0.50 M × alpha
4. Since propionic acid is a weak acid, we can assume that the concentration of [H+] will be equal to the concentration of [CH3CH2COO-].
5. To determine the concentration of [H+], we can use the equilibrium constant (Ka) expression for the dissociation of the acid:
Ka = [CH3CH2COO-] × [H+] / [propionic acid]
Ka = 1.3 × 10^-3 (given)
6. Substitute the known values into the Ka expression:
1.3 × 10^-3 = (0.50 M × alpha) × (0.50 M) / (0.50 M)
7. Solve for alpha (degree of dissociation):
alpha = (1.3 × 10^-3) / (0.50 × 0.50) = 0.0052
8. Now that we know the degree of dissociation (alpha), we can calculate the concentration of [H+] (which is equal to [CH3CH2COO-]):
[H+] = 0.50 M × 0.0052 = 0.0026 M
9. Finally, calculate the pH using the concentration of [H+]:
pH = -log[H+]
pH = -log(0.0026)
pH ≈ 2.59
Therefore, the pH of the solution containing 0.50 M propionic acid and 0.20 M sodium propionate is approximately 2.59.