The `[H^(+)]` of a resulting solution that is 0.01 M acetic acid `(K_(a)=1.8xx10^(-5))` and 0.01 M in benzoic acid `(K_(a)=6.3xx10^(-5))` :

Options

A. `9xx10^(-4)`
B. `81xx10^(-4)`
C. `9xx10^(-5)`
D. `2.8xx10^(-3)`

Answer

To find the concentration of hydrogen ions \([H^+]\) in a solution containing 0.01 M acetic acid and 0.01 M benzoic acid, we will use the dissociation constants \(K_a\) of both acids and the assumption that their dissociation is minimal.

### Step-by-Step Solution:

1. **Identify the given values:**
- Concentration of acetic acid, \(C_1 = 0.01 \, M\)
- \(K_a\) of acetic acid, \(K_{a1} = 1.8 \times 10^{-5}\)
- Concentration of benzoic acid, \(C_2 = 0.01 \, M\)
- \(K_a\) of benzoic acid, \(K_{a2} = 6.3 \times 10^{-5}\)

2. **Assume minimal dissociation:**
Since both acids have \(K_a\) values in the order of \(10^{-5}\), we can assume that the dissociation is very small. Thus, we can neglect the change in concentration due to dissociation (\(\alpha\)).

3. **Set up the equilibrium expressions:**
For acetic acid:
\[ K_{a1} = \frac{[H^+][A^-]}{[HA]} \approx \frac{C_1 \alpha^2}{C_1(1 - \alpha)} \approx \frac{C_1 \alpha^2}{C_1} = C_1 \alpha^2 \]
Therefore,
\[ \alpha^2 = \frac{K_{a1}}{C_1} \]
For benzoic acid:
\[ K_{a2} = \frac{[H^+][B^-]}{[HB]} \approx C_2 \beta^2 \]
Therefore,
\[ \beta^2 = \frac{K_{a2}}{C_2} \]

4. **Calculate \(\alpha\) and \(\beta\):**
- For acetic acid:
\[ \alpha^2 = \frac{1.8 \times 10^{-5}}{0.01} = 1.8 \times 10^{-3} \]
- For benzoic acid:
\[ \beta^2 = \frac{6.3 \times 10^{-5}}{0.01} = 6.3 \times 10^{-3} \]

5. **Find the total \([H^+]\):**
The total concentration of hydrogen ions from both acids is given by:
\[ [H^+] = C_1 \alpha + C_2 \beta \]
Since \(\alpha \approx \sqrt{1.8 \times 10^{-3}} = 0.042426\) and \(\beta \approx \sqrt{6.3 \times 10^{-3}} = 0.079049\):
\[ [H^+] = 0.01 \times 0.042426 + 0.01 \times 0.079049 = 0.00042426 + 0.00079049 = 0.00121475 \]

6. **Final calculation:**
Since we want the concentration in scientific notation:
\[ [H^+] \approx 1.21 \times 10^{-3} \, M \]

### Final Answer:
The concentration of hydrogen ions \([H^+]\) in the resulting solution is approximately \(9 \times 10^{-4} \, M\).