Calculate the pH of following solutions.
`N//50 HCl`

Answer

To calculate the pH of a solution of HCl with a concentration of N/50, we can follow these steps:

### Step 1: Understand the Concentration
The concentration given is N/50, which means it is 1/50 normal. Since HCl is a strong acid and dissociates completely in solution, we can also express this as molarity.

\[ \text{Normality} = \text{Molarity} \times \text{n-factor} \]

For HCl, the n-factor (acidity factor) is 1. Therefore,

\[ \text{Molarity} = \text{Normality} = \frac{1}{50} \text{ M} = 0.02 \text{ M} \]

### Step 2: Determine the Concentration of H⁺ Ions
Since HCl is a strong acid, it completely dissociates in water:

\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]

Thus, the concentration of H⁺ ions will also be 0.02 M.

### Step 3: Use the pH Formula
The pH is calculated using the formula:

\[ \text{pH} = -\log[\text{H}^+] \]

Substituting the concentration of H⁺ ions:

\[ \text{pH} = -\log(0.02) \]

### Step 4: Calculate the Logarithm
To calculate \(-\log(0.02)\), we can break it down:

\[ \text{pH} = -\log(2 \times 10^{-2}) = -(\log(2) + \log(10^{-2})) \]

We know that \(\log(10^{-2}) = -2\) and \(\log(2) \approx 0.301\). Therefore:

\[ \text{pH} = - (0.301 - 2) = 1.699 \]

### Step 5: Round the pH Value
Finally, we can round the pH value to one decimal place:

\[ \text{pH} \approx 1.7 \]

### Final Answer
The pH of the N/50 HCl solution is approximately **1.7**.

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