Enough of a monoprotic acid is dissolved in water to produce a 0.0192 M solution. The pH of the resulting solution is 2.53. Calculate the Ka for the acid.
The correct answer and explanation is :
To calculate the acid dissociation constant (Ka) for the monoprotic acid, we begin by interpreting the information given:
- Initial concentration of the acid: $HA$ = 0.0192 M
- The pH of the solution: pH = 2.53
- The acid is monoprotic, meaning it donates one proton (H⁺) per molecule.
Step 1: Calculate $H⁺$ from the pH
We use the formula:
$$
[H^+] = 10^{-\text{pH}} = 10^{-2.53} \approx 2.95 \times 10^{-3} \text{ M}
$$
This is the concentration of dissociated H⁺ ions, which equals the concentration of the conjugate base $[A^-]$, because the acid is monoprotic.
Step 2: Use an ICE Table
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HA | 0.0192 | -x | 0.0192 – x |
| H⁺ | 0 | +x | x = 2.95 × 10⁻³ |
| A⁻ | 0 | +x | x = 2.95 × 10⁻³ |
So, at equilibrium:
$$
[HA] = 0.0192 – 0.00295 = 0.01625 \text{ M}
$$
Step 3: Use the Ka Expression
$$
K_a = \frac{[H^+][A^-]}{[HA]} = \frac{(2.95 \times 10^{-3})^2}{0.01625}
$$
$$
K_a = \frac{8.70 \times 10^{-6}}{0.01625} \approx 5.35 \times 10^{-4}
$$
Final Answer:
$$
\boxed{K_a = 5.35 \times 10^{-4}}
$$
Explanation (300 Words):
The acid dissociation constant, Ka, is a measure of the strength of an acid in solution. It represents the equilibrium constant for the dissociation of an acid (HA) into hydrogen ions (H⁺) and its conjugate base (A⁻). In this problem, we are given the concentration of a monoprotic acid solution and its pH, and we are asked to determine Ka.
We start by using the pH value to determine the concentration of hydrogen ions. pH is the negative logarithm of the hydrogen ion concentration, so using the inverse logarithmic function gives us [H⁺]. For a monoprotic acid, the concentration of [H⁺] is equal to the concentration of the conjugate base [A⁻] because each molecule of acid that dissociates produces one H⁺ and one A⁻.
Next, we consider how much of the acid has dissociated. We subtract the amount dissociated from the initial acid concentration to get the equilibrium concentration of the undissociated acid [HA].
We then use the Ka expression, which is derived from the law of mass action. Plugging in the equilibrium concentrations, we calculate Ka. This value gives us insight into the acid’s strength. A larger Ka means a stronger acid (more dissociation), while a smaller Ka indicates a weaker acid (less dissociation).
In this case, the Ka value of approximately 5.35 × 10⁻⁴ suggests the acid is weak but partially dissociates in solution.