What will be the pH of the resulting solution if to a 100 ml of HCl solution of pH = 1.0, 900 ml of distilled water is added ?

Explanation

To find the pH of the resulting solution after diluting a 100 ml HCl solution with a pH of 1.0 by adding 900 ml of distilled water, we can follow these steps:

### Step 1: Determine the concentration of H⁺ ions in the original solution.
Given that the pH of the HCl solution is 1.0, we can use the formula for pH:

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

From this, we can find the concentration of H⁺ ions:

\[ 1.0 = -\log[H^+] \]

Taking the antilogarithm:

\[ [H^+] = 10^{-1} \, \text{M} = 0.1 \, \text{M} \]

### Step 2: Calculate the number of moles of H⁺ in the original solution.
Using the concentration and volume of the original solution, we can calculate the moles of H⁺:

\[ \text{Moles of } H^+ = [H^+] \times \text{Volume} = 0.1 \, \text{mol/L} \times 0.1 \, \text{L} = 0.01 \, \text{mol} \]

### Step 3: Determine the total volume of the resulting solution.
After adding 900 ml of distilled water to the original 100 ml of HCl solution, the total volume becomes:

\[ \text{Total Volume} = 100 \, \text{ml} + 900 \, \text{ml} = 1000 \, \text{ml} = 1 \, \text{L} \]

### Step 4: Calculate the new concentration of H⁺ ions in the diluted solution.
The number of moles of H⁺ remains the same, but the volume has increased. The new concentration of H⁺ ions is:

\[ [H^+] = \frac{\text{Moles of } H^+}{\text{Total Volume}} = \frac{0.01 \, \text{mol}}{1 \, \text{L}} = 0.01 \, \text{M} \]

### Step 5: Calculate the new pH of the resulting solution.
Now, we can find the pH of the diluted solution using the concentration of H⁺ ions:

\[ \text{pH} = -\log[H^+] = -\log(0.01) = 2.0 \]

### Final Answer:
The pH of the resulting solution after dilution is **2.0**.

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