Chapter 3.4, Problem 5TY

Interpretation Introduction

Interpretation:

When the uncertainty in given pH is doubled, the relative uncertainty in ${\text{[H}}^{\text{+}}\text{]}$ has to be calculated.

Concept Introduction:

Exponents and logarithm:

Consider, $y=\text{antilog }x\Rightarrow y={10}^x$ .

Here, the relative uncertainty in y is proportional to the absolute uncertainty in x.

$\begin{array}{l}{\text{Uncertainty for 10}}^{x:}\\ y={10}^x\\ \Rightarrow \frac{e_y}{y}=(\text{ln 10)}{e}_x\\ \approx 2.3026e_x\end{array}$

To Calculate: The relative uncertainty in ${\text{[H}}^{\text{+}}\text{]}$ when the uncertainty in given pH is doubled.