The pH of a solution is a measure of its acidity. Formally, pH = -0.4343lna where a is the hydrogen ion activity.

Question

The pH of a solution is a measure of its acidity. Formally, pH = -0.4343lna where a is the hydrogen ion activity. Suppose that the hydrogen ion activity of a solution is increasing at a rate of 0.003/minute. How quickly is the pH decreasing when the hydrogen ion activity is 0.02?

Answer 1

Let P = pH = -0.4343(lna)

Given: dA/dt = 0.003 and a = 0.02

Find: dP/dt

dP/dt = -0.4343(1/a)(dA/dt) = -0.4343(50)(0.003) ≈ 0.065

The pH is increasing at the rate of approximately 0.065 units/minute when a = 0.02 and dA/dt = 0.003.