Question

Some effervescent tablets (like Alka-Seltzer) contain aspirin that dissolves when plopped into a glass of water. If a tablet contains 325 mg of aspirin and is dissolved in water to make 100 mL solution, what is the hydronium (H ) ion concentration?

Answer 1

Answer: The concentration of hydronium ion in the solution is 0.00225 M

Explanation:

To calculate the molarity of solution, we use the equation:

$\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}$

Given mass of aspirin = 325 mg = 0.325 g    (Conversion factor: 1 g = 1000 mg)

Molar mass of aspirin = 180.16 g/mol

Volume of solution = 100 mL

Putting values in above equation, we get:

$\text{Molarity of solution}=\frac{0.325\times 1000}{180.16\times 100}\\\\\text{Molarity of solution}=0.0180M$

The chemical equation for the reaction of aspirin with water follows:

                            $C_9H_8O_4+H_2O\rightleftharpoons C_9H_7O_4^-+H_3O^+$

Initial:                    0.0180

At eqllm:             0.0180-x                       x             x

The expression of $K_a$ for above equation follows:

$K_a=\frac{[C_9H_7O^-][H_3O^+]}{[C_9H_8O_4]}$

We know that:

$K_a\text{ for aspirin}=3.24\times 10^{-4}$

Putting values in above expression, we get:

$3.24\times 10^{-4}=\frac{x\times x}{0.0180-x}\\\\x=0.00225,-0.00258$

Neglecting the negative value of 'x' because concentration cannot be negative.

$H_3O^+=x=0.00225M$

Hence, the concentration of hydronium ion in the solution is 0.00225 M