Respuesta :
Answer: The concentration of hydronium ion in the solution is 0.00225 M
Explanation:
To calculate the molarity of solution, we use the equation:
[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}[/tex]
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:
[tex]\text{Molarity of solution}=\frac{0.325\times 1000}{180.16\times 100}\\\\\text{Molarity of solution}=0.0180M[/tex]
The chemical equation for the reaction of aspirin with water follows:
[tex]C_9H_8O_4+H_2O\rightleftharpoons C_9H_7O_4^-+H_3O^+[/tex]
Initial: 0.0180
At eqllm: 0.0180-x x x
The expression of [tex]K_a[/tex] for above equation follows:
[tex]K_a=\frac{[C_9H_7O^-][H_3O^+]}{[C_9H_8O_4]}[/tex]
We know that:
[tex]K_a\text{ for aspirin}=3.24\times 10^{-4}[/tex]
Putting values in above expression, we get:
[tex]3.24\times 10^{-4}=\frac{x\times x}{0.0180-x}\\\\x=0.00225,-0.00258[/tex]
Neglecting the negative value of 'x' because concentration cannot be negative.
[tex]H_3O^+=x=0.00225M[/tex]
Hence, the concentration of hydronium ion in the solution is 0.00225 M
