Question

If the pH of a solution is 2.78 with an absolute uncertainty of ±0.05, what is the LaTeX: \left[H^+\right][ H + ] and its uncertainty?

Answer 1

Answer:

[H⁺] = 16.6 (±1.9) x10⁻⁴ M

Explanation:

The pH is defined as:

• pH = -log[H⁺]

So we can calculate [H⁺]:

• 2.78 = -log[H⁺]

• -2.78 = log[H⁺]

• [H⁺] = $10^{-2.78}$

[H⁺] = 1.66x10⁻³ M

The relative uncertainty in [H⁺] is

• uR/R = 2.303 x AbsoluteUncertainty

• uR/R = 2.303 * 0.05 = 0.115

Thus the uncertainty in the concentration is:

1.66x10⁻³ M * 0.115 = 1.91x10⁻⁴ M