Which of the following solution will have pOH equal to 11 at 298 K

Options

A. `1xx10^(-11) M` HCl
B. `1xx10^(-3) HCl`
C. `1xx10^(-3)` NaOH
D. pOH of solution cannot be 11

Explanation

To determine which of the given solutions will have a pOH equal to 11 at 298 K, we will follow these steps:

### Step 1: Understand the relationship between pH and pOH
The relationship between pH and pOH is given by the equation:
\[ \text{pH} + \text{pOH} = 14 \]

### Step 2: Calculate the corresponding pH for pOH = 11
If we know that pOH = 11, we can find the pH using the equation from Step 1:
\[ \text{pH} = 14 - \text{pOH} = 14 - 11 = 3 \]

### Step 3: Analyze the options provided
We have the following options:
1. \( 10^{-11} \, \text{M HCl} \)
2. \( 10^{-3} \, \text{M HCl} \)
3. \( 10^{-3} \, \text{M NaOH} \)
4. pOH of the solution cannot be 11

### Step 4: Calculate the pH and pOH for each option

**Option 1: \( 10^{-11} \, \text{M HCl} \)**
- HCl is a strong acid and completely dissociates:
\[ [\text{H}^+] = 10^{-11} \, \text{M} \]
- Calculate pH:
\[ \text{pH} = -\log(10^{-11}) = 11 \]
- Calculate pOH:
\[ \text{pOH} = 14 - \text{pH} = 14 - 11 = 3 \]

**Option 2: \( 10^{-3} \, \text{M HCl} \)**
- HCl is a strong acid and completely dissociates:
\[ [\text{H}^+] = 10^{-3} \, \text{M} \]
- Calculate pH:
\[ \text{pH} = -\log(10^{-3}) = 3 \]
- Calculate pOH:
\[ \text{pOH} = 14 - \text{pH} = 14 - 3 = 11 \]

**Option 3: \( 10^{-3} \, \text{M NaOH} \)**
- NaOH is a strong base and completely dissociates:
\[ [\text{OH}^-] = 10^{-3} \, \text{M} \]
- Calculate pOH:
\[ \text{pOH} = -\log(10^{-3}) = 3 \]
- Calculate pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 3 = 11 \]

**Option 4: pOH of the solution cannot be 11**
- This option is not valid since we have found a solution with pOH = 11.

### Step 5: Conclusion
From the calculations, we see that the solution that has a pOH equal to 11 is:
- **Option 2: \( 10^{-3} \, \text{M HCl} \)**