Answer
(c) 2.32
Work Step by Step
1. Draw the ICE table for this equilibrium:
$$\begin{vmatrix}
Compound& [ HC_7H_5O_2 ]& [ C_7H_5{O_2}^- ]& [ H_3O^+ ]\\
Initial& 0.350 & 0 & 0 \\
Change& -x& +x& +x\\
Equilibrium& 0.350 -x& 0 +x& 0 +x\\
\end{vmatrix}$$
2. Write the expression for $K_a$, and substitute the concentrations:
- The exponent of each concentration is equal to its balance coefficient.
$$K_a = \frac{[Products]}{[Reactants]} = \frac{[ C_7H_5{O_2}^- ][ H_3O^+ ]}{[ HC_7H_5O_2 ]}$$
$$K_a = \frac{(x)(x)}{[ HC_7H_5O_2 ]_{initial} - x}$$
3. Assuming $ 0.350 \gt\gt x:$
$$K_a = \frac{x^2}{[ HC_7H_5O_2 ]_{initial}}$$
$$x = \sqrt{K_a \times [ HC_7H_5O_2 ]_{initial}} = \sqrt{ 6.5 \times 10^{-5} \times 0.350 }$$
$x = 4.8 \times 10^{-3} $
4. Test if the assumption was correct:
$$\frac{ 4.8 \times 10^{-3} }{ 0.350 } \times 100\% = 1.4 \%$$
5. The percent is less than 5%. Thus, it is correct to say that $x = 4.8 x 10^{-3} $
6. $$[H_3O^+] = x = 4.8 \times 10^{-3} $$
7. Calculate the pH:
$$pH = -log[H_3O^+] = -log( 4.8 \times 10^{-3} ) = 2.32 $$
