A solution of an acid has `pH= 4.70`. Find out the concentration of `OH^(-)` ions `(pK_(w)=14)`.

Options

A. `5xx10^(-10)`
B. `6xx10^(-10)`
C. `2xx10^(-6)`
D. `9xx10^(-10)`

Answer

To find the concentration of hydroxide ions (OH⁻) in a solution with a given pH of 4.70, we can follow these steps:

### Step 1: Understand the relationship between pH, pOH, and pKw
We know that:
\[ \text{pH} + \text{pOH} = \text{pK}_w \]
where \( \text{pK}_w \) is the ion product of water at 25°C, which is 14.

### Step 2: Calculate pOH
Given that the pH is 4.70, we can calculate pOH as follows:
\[ \text{pOH} = \text{pK}_w - \text{pH} \]
Substituting the values:
\[ \text{pOH} = 14 - 4.70 = 9.30 \]

### Step 3: Relate pOH to the concentration of OH⁻ ions
The concentration of hydroxide ions can be found using the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
To find the concentration of OH⁻ ions, we rearrange this equation:
\[ [\text{OH}^-] = 10^{-\text{pOH}} \]

### Step 4: Substitute the pOH value
Now substituting the pOH value we calculated:
\[ [\text{OH}^-] = 10^{-9.30} \]

### Step 5: Calculate the concentration
Using a calculator:
\[ [\text{OH}^-] = 10^{-9.30} \approx 5.01 \times 10^{-10} \, \text{mol/L} \]

### Final Answer
The concentration of hydroxide ions (OH⁻) in the solution is approximately:
\[ [\text{OH}^-] \approx 5.0 \times 10^{-10} \, \text{mol/L} \]

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