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 need to follow a systematic approach. Here is the step-by-step breakdown of how we calculate Ka.
1. Given information:
- The concentration of the acid solution: [HA] = 0.0192 M.
- The pH of the solution: pH = 2.53.
2. Determine [H⁺] from pH:
The pH of a solution is related to the concentration of hydrogen ions ([H⁺]) by the following formula:
[
\text{pH} = -\log[\text{H}^+]
]
We can rearrange the formula to solve for [H⁺]:
[
[\text{H}^+] = 10^{-\text{pH}}
]
Substituting the given pH of 2.53:
[
[\text{H}^+] = 10^{-2.53} \approx 2.97 \times 10^{-3} \, \text{M}
]
3. Set up the equilibrium expression:
The dissociation of the monoprotic acid (HA) can be represented as:
[
\text{HA (aq)} \rightleftharpoons \text{H}^+ (aq) + \text{A}^- (aq)
]
The initial concentration of HA is 0.0192 M, and at equilibrium, a portion of the HA dissociates into H⁺ and A⁻. Let the concentration of dissociated acid at equilibrium be denoted as x. Thus, we have:
- [H⁺] = x
- [A⁻] = x
- [HA] = 0.0192 – x From the pH calculation, we already know [H⁺] = 2.97 × 10⁻³ M, which means x = 2.97 × 10⁻³ M.
4. Write the expression for Ka:
The equilibrium expression for the acid dissociation constant (Ka) is:
[
K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}
]
Substituting the values into the Ka expression:
[
K_a = \frac{(2.97 \times 10^{-3})(2.97 \times 10^{-3})}{0.0192 – 2.97 \times 10^{-3}}
]
Simplifying:
[
K_a = \frac{(2.97 \times 10^{-3})^2}{0.0192 – 2.97 \times 10^{-3}} = \frac{8.82 \times 10^{-6}}{0.01623}
]
[
K_a \approx 5.44 \times 10^{-4}
]
Conclusion:
The acid dissociation constant, Ka, for the monoprotic acid is approximately 5.44 × 10⁻⁴.
Explanation:
- pH and [H⁺] relationship: The pH provides information about the concentration of hydrogen ions in the solution. Since the pH was given as 2.53, we could directly calculate [H⁺], which helps us to understand the extent of dissociation of the acid.
- ICE Table and assumptions: By setting up an ICE (Initial, Change, Equilibrium) table, we calculate the concentration of dissociated acid, which is crucial for determining the Ka.
- Ka Expression: The Ka expression is derived from the dissociation of the acid into H⁺ and A⁻ ions. By knowing the concentrations of these ions and the undissociated acid at equilibrium, we can solve for the value of Ka. The relatively small value of Ka indicates that the acid is weak, meaning it only partially dissociates in solution.