Calculate the hydrogen ion concentration (`"in mol"//dm^3`) in a solution containing 0.04 mole of acetic acid and 0.05 mole of sodium acetate in 500 mL of solution.Dissociation constant for acetic acid is `1.75xx10^(-6)` Report your answer after multiplying by `2xx10^(6)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Moles of acetic acid (CH₃COOH) = 0.04 mol
- Moles of sodium acetate (CH₃COONa) = 0.05 mol
- Volume of solution = 500 mL = 0.5 L
- Dissociation constant (Kₐ) for acetic acid = 1.75 x 10^(-6)

### Step 2: Calculate the concentrations of acetic acid and sodium acetate
To find the concentrations, we use the formula:
\[ \text{Concentration} = \frac{\text{Number of moles}}{\text{Volume in L}} \]

- Concentration of acetic acid (C₁):
\[ C_{1} = \frac{0.04 \text{ mol}}{0.5 \text{ L}} = 0.08 \text{ mol/dm}^3 \]

- Concentration of sodium acetate (C₂):
\[ C_{2} = \frac{0.05 \text{ mol}}{0.5 \text{ L}} = 0.1 \text{ mol/dm}^3 \]

### Step 3: Calculate pKa from the dissociation constant (Kₐ)
We can find pKa using the formula:
\[ pK_a = -\log(K_a) \]
Substituting the value of Kₐ:
\[ pK_a = -\log(1.75 \times 10^{-6}) \approx 5.75 \]

### Step 4: Use the Henderson-Hasselbalch equation
The Henderson-Hasselbalch equation for a buffer solution is:
\[ pH = pK_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
Substituting the values:
\[ pH = 5.75 + \log\left(\frac{0.1}{0.08}\right) \]
Calculating the log term:
\[ \log\left(\frac{0.1}{0.08}\right) = \log(1.25) \approx 0.0969 \]
Now substituting back into the pH equation:
\[ pH = 5.75 + 0.0969 \approx 5.8469 \]

### Step 5: Calculate the hydrogen ion concentration
Using the pH to find the hydrogen ion concentration:
\[ [\text{H}^+] = 10^{-pH} = 10^{-5.8469} \approx 1.4 \times 10^{-6} \text{ mol/dm}^3 \]

### Step 6: Multiply by \(2 \times 10^6\)
Finally, we multiply the hydrogen ion concentration by \(2 \times 10^6\):
\[ [\text{H}^+] \times 2 \times 10^6 = 1.4 \times 10^{-6} \times 2 \times 10^6 = 2.8 \]

### Final Answer
The hydrogen ion concentration is **2.8**.

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