What is the pH value of `N/10^(7) KOH` solution?

Options

A. 7
B. between 7 and 8
C. 8
D. between 6 and 7

Explanation

To find the pH value of a `N/10^(7) KOH` solution, we can follow these steps:

### Step 1: Understand the concentration of KOH
The concentration of KOH is given as `N/10^(7)`, which can be expressed as `10^(-7) N`. Since KOH is a strong base, it completely dissociates in water to give K⁺ and OH⁻ ions.

### Step 2: Calculate the concentration of OH⁻ ions
From the dissociation of KOH:
- The concentration of OH⁻ ions from KOH = `10^(-7) M`.

### Step 3: Consider the contribution of water
Water also dissociates into H⁺ and OH⁻ ions:
- The ion product of water (Kw) at 25°C is `10^(-14)`.
- Therefore, the concentration of H⁺ ions in pure water is `10^(-7) M`.

### Step 4: Total concentration of OH⁻ ions
Since the solution contains both the OH⁻ ions from KOH and from water, we need to add these contributions:
- Total concentration of OH⁻ ions = `10^(-7) + 10^(-7) = 2 × 10^(-7) M`.

### Step 5: Calculate the concentration of H⁺ ions
Using the ion product of water:
\[ K_w = [H^+][OH^-] \]
\[ 10^{-14} = [H^+][2 \times 10^{-7}] \]
To find [H⁺]:
\[ [H^+] = \frac{10^{-14}}{2 \times 10^{-7}} = 0.5 \times 10^{-7} = 5 \times 10^{-8} M \]

### Step 6: Calculate the pH
The pH is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
Substituting the value of [H⁺]:
\[ \text{pH} = -\log(5 \times 10^{-8}) \]
Using logarithmic properties:
\[ \text{pH} = -\log(5) - \log(10^{-8}) \]
\[ \text{pH} = -0.699 + 8 \]
\[ \text{pH} \approx 7.301 \]

### Conclusion
The pH value of the `N/10^(7) KOH` solution is approximately 7.3, which indicates it is slightly basic.

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