A hydrogen electrode placed in a solution containing sodium acetate and acetic acid in the ratio of `x:y` and `y:x`, ahs electrode potential values of `-1.5` and `-0.5V`, respectively. What is the `pK_(a)` value of acetic acid?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
We have a hydrogen electrode placed in a solution of sodium acetate and acetic acid in two different ratios: \(x:y\) and \(y:x\). The electrode potentials for these two ratios are given as \(-1.5V\) and \(-0.5V\), respectively.

### Step 2: Write the Nernst equation for both cases
For a weak acid (acetic acid) and its salt (sodium acetate), we can use the Henderson-Hasselbalch equation to relate pH, pKa, and the concentrations of the acid and its salt:

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