To a solution of acetic acid, solid sodium acetate is gradually added. When '' of the salt has been — Ionic Equilibrium Chemistry Question
Question
To a solution of acetic acid, solid sodium acetate is gradually added. When '$x \text{ g}$' of the salt has been added, the pH has a certain value. When total '$y \text{ g}$' of the salt has been added, the pH has been further raised by 0.6 units. What is the ratio of $x:y$? ($\log 3.98 = 0.6$)
💡 Solution & Explanation
Let the moles of acid be $m_{\text{acid}}$. With $x$ grams of salt, $\text{pH}_1 = pK_a + \log(x / m_{\text{acid}})$. With $y$ grams of salt, $\text{pH}_2 = pK_a + \log(y / m_{\text{acid}})$. We are given $\text{pH}_2 - \text{pH}_1 = 0.6$. Substituting the expressions: $\log(y / m_{\text{acid}}) - \log(x / m_{\text{acid}}) = 0.6 \implies \log(y/x) = 0.6$. Given $\log 3.98 = 0.6$, this means $y/x = 3.98$. The asked ratio is $x:y$, which is $1:3.98$. Therefore, correct answer is B.