What is pOH of an aqueous solution with hydrogen ion concentration equal to `3xx10^(-5)" mol L"^(-1)`?

Options

A. a. 9.47
B. b. 4.52
C. c. 12.69
D. d. 11.69

Explanation

To find the pOH of an aqueous solution with a hydrogen ion concentration of \(3 \times 10^{-5} \, \text{mol L}^{-1}\), we can follow these steps:

### Step 1: Calculate pH
The pH of a solution can be calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
Given that the hydrogen ion concentration \([\text{H}^+]\) is \(3 \times 10^{-5} \, \text{mol L}^{-1}\), we can substitute this value into the formula.

### Step 2: Substitute the value into the pH formula
\[ \text{pH} = -\log(3 \times 10^{-5}) \]

### Step 3: Break down the logarithm
Using the properties of logarithms, we can separate the terms:
\[ \text{pH} = -\log(3) - \log(10^{-5}) \]
\[ \text{pH} = -\log(3) + 5 \]

### Step 4: Calculate \(-\log(3)\)
The value of \(-\log(3)\) is approximately \(-0.477\). Therefore:
\[ \text{pH} = -0.477 + 5 \]
\[ \text{pH} = 4.523 \]

### Step 5: Calculate pOH using the relationship between pH and pOH
The relationship between pH and pOH is given by:
\[ \text{pH} + \text{pOH} = 14 \]
Substituting the calculated pH value:
\[ 4.523 + \text{pOH} = 14 \]

### Step 6: Solve for pOH
Rearranging the equation gives:
\[ \text{pOH} = 14 - 4.523 \]
\[ \text{pOH} = 9.477 \]

### Final Answer
The pOH of the solution is approximately \(9.477\).

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