pH of HCI is 2.1. what is `[OH^(-)]` in its solution?

Options

A. `1.259 xx 10^(-12)` mol/I
B. `1.259 xx 10^(-12) g//dm^(3)`
C. `12.6 xx 10^(-12)` mol/I
D. `12.59 xx 10^(-12) g//dm^(3)`

Answer

To find the hydroxyl ion concentration \([OH^-]\) in a solution of HCl with a pH of 2.1, we can follow these steps:

### Step 1: Calculate the Hydrogen Ion Concentration \([H^+]\)
The pH is defined as:
\[ \text{pH} = -\log[H^+] \]
Given that the pH of the solution is 2.1, we can rearrange the formula to find \([H^+]\):
\[ [H^+] = 10^{-\text{pH}} = 10^{-2.1} \]

### Step 2: Calculate the Value of \([H^+]\)
Now we calculate:
\[ [H^+] = 10^{-2.1} \approx 0.0079 \, \text{mol/L} \]

### Step 3: Use the Ion Product of Water to Find \([OH^-]\)
At 25°C, the ion product of water (\(K_w\)) is:
\[ K_w = [H^+][OH^-] = 1.0 \times 10^{-14} \]
We can rearrange this equation to solve for \([OH^-]\):
\[ [OH^-] = \frac{K_w}{[H^+]} \]

### Step 4: Substitute the Values
Now we substitute the values we have:
\[ [OH^-] = \frac{1.0 \times 10^{-14}}{0.0079} \]

### Step 5: Calculate \([OH^-]\)
Calculating this gives:
\[ [OH^-] \approx 1.27 \times 10^{-12} \, \text{mol/L} \]

### Final Answer
Thus, the hydroxyl ion concentration \([OH^-]\) in the solution is approximately:
\[ [OH^-] \approx 1.26 \times 10^{-12} \, \text{mol/L} \]

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