Given that the value of Kw for water is 1 x 10-14, what is the pH of a 0.001 molar KOH solution?

a. 10-11

c. 3

b. 10-3 d. 11

To determine the pH of a 0.001 molar (M) KOH solution, let's first recognize that KOH is a strong base and fully dissociates in water:

\[ \text{KOH} \rightarrow \text{K}^+ + \text{OH}^- \]

Since the concentration of KOH is 0.001 M, the concentration of \(\text{OH}^-\) ions in the solution is also 0.001 M.

Next, we use the relationship between the concentrations of \(\text{H}^+\) and \(\text{OH}^-\) ions, given by the water dissociation constant (\(K_w\)):

\[ K_w = [\text{H}^+][\text{OH}^-] \]

Given \( K_w = 1 \times 10^{-14} \):

\[ [\text{H}^+] = \frac{K_w}{[\text{OH}^-]} \]

Substitute the values:

\[ [\text{H}^+] = \frac{1 \times 10^{-14}}{0.001} = \frac{1 \times 10^{-14}}{1 \times 10^{-3}} = 1 \times 10^{-11} \text{ M} \]

Finally, to find the pH:

\[ \text{pH} = -\log[\text{H}^+] = -\log(1 \times 10^{-11}) = 11 \]

So, the pH of the solution is **11**.

The correct answer is **d. 11**.

Would you like details or have any questions? Here are some related questions:

1. How does the dissociation of strong acids and bases differ in water?
2. What is the significance of the water dissociation constant, \(K_w\)?
3. How does the pH scale relate to the concentration of hydrogen ions?
4. What happens to the pH of a solution when a strong acid is added to a strong base?
5. How do you calculate the pOH of a solution?

**Tip:** Remember, pH + pOH = 14 in pure water at 25°C. This is useful for finding pH when you know the concentration of \(\text{OH}^-\).

Learn how to calculate the pH of a 0.001 molar KOH solution using the dissociation constant of water (Kw). Follow a step-by-step solution explaining pH calculations and the relationship between hydrogen ion concentration and hydroxide ion concentration. Suitable for advanced high school students studying chemistry.

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