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 $K_a$ (acid dissociation constant) of a monoprotic acid from the given data, we will use the following information:
- Concentration of acid ($[HA]$) = 0.0192 M
- pH of the solution = 2.53
Step 1: Calculate the concentration of hydrogen ions ($[H^+]$)
We know that the pH is related to the concentration of hydrogen ions by the formula:
$$
\text{pH} = -\log[H^+]
$$
Given the pH is 2.53, we can solve for $[H^+]$:
$$
[H^+] = 10^{-\text{pH}} = 10^{-2.53} \approx 2.95 \times 10^{-3} \, \text{M}
$$
Step 2: Set up an ICE table for the dissociation of the monoprotic acid (HA)
The dissociation of the monoprotic acid in water can be represented as:
$$
HA \rightleftharpoons H^+ + A^-
$$
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| $HA$ | 0.0192 | -x | $0.0192 – x$ |
| $H^+$ | 0 | +x | $x = 2.95 \times 10^{-3}$ |
| $A^-$ | 0 | +x | $x = 2.95 \times 10^{-3}$ |
From the ICE table, $x$ represents the concentration of $H^+$, which is $2.95 \times 10^{-3} \, \text{M}$.
Step 3: Write the expression for the acid dissociation constant ($K_a$)
The expression for $K_a$ is:
$$
K_a = \frac{[H^+][A^-]}{[HA]}
$$
Substitute the known values into the expression:
$$
K_a = \frac{(2.95 \times 10^{-3})(2.95 \times 10^{-3})}{0.0192 – 2.95 \times 10^{-3}}
$$
$$
K_a = \frac{(2.95 \times 10^{-3})^2}{0.01625}
$$
$$
K_a = \frac{8.70 \times 10^{-6}}{0.01625} \approx 5.36 \times 10^{-4}
$$
Final Answer:
The acid dissociation constant $K_a$ for the acid is approximately $5.36 \times 10^{-4}$.
Explanation:
In this problem, the pH is used to find the concentration of hydrogen ions ($H^+$), which allows us to determine the extent of dissociation of the monoprotic acid. By setting up an ICE table for the dissociation of the acid and applying the expression for $K_a$, we can calculate the acid dissociation constant. This value tells us how strongly the acid dissociates in water: a higher $K_a$ indicates a stronger acid, while a lower value indicates a weaker acid.