If `H_(3)O^(+)` ion concentration of a solution is increased by 10 times , its pH will

Options

A. Increase by `1`
B. Remains unchanged
C. Decreases by `1`
D. Increase by `10`

Explanation

To solve the problem of how the pH changes when the hydronium ion concentration increases by 10 times, we can follow these steps:

### Step 1: Understand the Relationship Between pH and Hydronium Ion Concentration
The pH of a solution is defined as:
\[ \text{pH} = -\log[H_3O^+] \]
where \([H_3O^+]\) is the concentration of hydronium ions in moles per liter.

### Step 2: Define the Initial Hydronium Ion Concentration
Let’s denote the initial concentration of hydronium ions as \([H_3O^+] = C\). Therefore, the initial pH can be expressed as:
\[ \text{pH} = -\log C \]

### Step 3: Calculate the New Hydronium Ion Concentration
If the hydronium ion concentration is increased by 10 times, the new concentration will be:
\[ [H_3O^+] = 10C \]

### Step 4: Calculate the New pH
Using the new concentration, we can find the new pH:
\[ \text{pH}_{\text{new}} = -\log(10C) \]

### Step 5: Apply Logarithmic Properties
Using the logarithmic property that states \(\log(ab) = \log a + \log b\), we can rewrite the new pH:
\[ \text{pH}_{\text{new}} = -\log(10) - \log(C) \]
Since \(\log(10) = 1\), we have:
\[ \text{pH}_{\text{new}} = -1 - \log(C) \]
This can be simplified to:
\[ \text{pH}_{\text{new}} = \text{pH} - 1 \]

### Step 6: Conclusion
Thus, when the hydronium ion concentration increases by 10 times, the pH decreases by 1 unit.

### Final Answer
If the hydronium ion concentration of a solution is increased by 10 times, its pH will decrease by 1.

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