pH of a mixture of 1 M benzoic acid (pKa = 4.20) and 1 M sodium benzoa...
pH of the mixture: The pH of a buffer solution is determined by the equilibrium between the weak acid and its conjugate base. In this case, benzoic acid (weak acid) and sodium benzoate (conjugate base) are present in the mixture. The pKa of benzoic acid is given as 4.20. The pH of the mixture is 4.5.
Buffer solution: A buffer solution is a solution that resists changes in pH when small amounts of acid or base are added. It is composed of a weak acid and its conjugate base (or a weak base and its conjugate acid).
Henderson-Hasselbalch equation: The Henderson-Hasselbalch equation is used to calculate the pH of a buffer solution. It is given as:
pH = pKa + log([A-]/[HA])
Where pH is the desired pH of the buffer, pKa is the dissociation constant of the weak acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.
Calculating the ratio: In this case, the pH of the mixture is 4.5, and the pKa of benzoic acid is 4.20. Plugging these values into the Henderson-Hasselbalch equation, we can solve for the ratio [A-]/[HA].
4.5 = 4.20 + log([A-]/[HA])
0.3 = log([A-]/[HA])
[A-]/[HA] = 10^0.3
[A-]/[HA] = 1.995
Calculating the concentrations: Since we know that the initial concentrations of benzoic acid and sodium benzoate are both 1 M, we can set up the following equation:
[A-]/[HA] = [sodium benzoate]/[benzoic acid]
1.995 = [sodium benzoate]/[benzoic acid]
Calculating the volume of benzoic acid: Since the total volume of the buffer is 300 mL, we can set up the following equation:
[benzoic acid] + [sodium benzoate] = 300 mL
[benzoic acid] + 1 = 300 mL
[benzoic acid] = 300 mL - 1
[benzoic acid] = 299 mL
Substituting the values: Substituting the value of [benzoic acid] into the concentration equation, we can solve for [sodium benzoate].
1.995 = [sodium benzoate]/299
[sodium benzoate] = 1.995 * 299
[sodium benzoate] = 597.305
Calculating the