The pH of a solution is 5. Its hydrogen ion concentration is increased 100 times. What is the pH of the resulting solution ?

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the relationship between pH and hydrogen ion concentration.
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in moles per liter.

### Step 2: Calculate the initial hydrogen ion concentration.
Given that the pH of the solution is 5, we can find the initial hydrogen ion concentration:
\[ 5 = -\log[H^+] \]
To find \([H^+]\), we rearrange this equation:
\[ [H^+] = 10^{-5} \, \text{mol/L} \]

### Step 3: Increase the hydrogen ion concentration 100 times.
If the hydrogen ion concentration is increased 100 times, we multiply the initial concentration by 100:
\[ [H^+]_{\text{new}} = 100 \times 10^{-5} = 10^{-3} \, \text{mol/L} \]

### Step 4: Calculate the new pH.
Now we can calculate the new pH using the new hydrogen ion concentration:
\[ \text{pH}_{\text{new}} = -\log[H^+]_{\text{new}} = -\log(10^{-3}) \]
Calculating this gives:
\[ \text{pH}_{\text{new}} = 3 \]

### Final Answer:
The pH of the resulting solution after increasing the hydrogen ion concentration 100 times is **3**.

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