Chapter 3, Problem 3.15P

(a)

Interpretation Introduction

Interpretation:

The $\left[H^{+}\right]$ value of solution and also its uncertainty have to be calculated.

Concept Introduction:

• pH of a solution is the negative of the base $\text{-10}$ logarithm of the hydronium ion or hydrogen ion concentration.

  $\begin{array}{l}\text{pH}\text{=}\text{-log}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\\ \text{pH}\text{=}\text{-log}\left[{\text{H}}^{\text{+}}\right]\end{array}$

• Concentration of hydrogen ion $\left[{\text{H}}^{\text{+}}\right]\text{=}{\text{10}}^{\text{-pH}}$

Uncertainty in $pH$and$\left[H^{+}\right]$:

  $\begin{array}{l}\text{Uncertainty in }\left[{\text{H}}^{\text{+}}\right]\text{=}\text{2}\text{.303}\left[{\text{H}}^{\text{+}}\right]\left(\text{Uncertainty}\text{in }\text{pH}\right)\\ \\ \text{where,}\text{2}\text{.303}\text{is}\text{the}\text{natural}\text{logarithm}\text{of}\text{10}\text{.}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The relative uncertainty in $\left[{\text{H}}^{\text{+}}\right]$ has to be calculated.

Concept Introduction:

Uncertainty:

Uncertainty means state of not certain in predicting a value.  In a measured value, the last digit will have associated uncertainty. Uncertainty has two values, absolute uncertainty and relative uncertainty.

Absolute uncertainty:

  Expressed the marginal value associated with a measurement

Relative uncertainty:

Compares the size of absolute uncertainty with the size of its associated measurement

  $\text{Relative uncertainty = }\frac{\text{absolute uncertainty}}{\text{magnitude of measurement}}$

(c)

Interpretation Introduction

Interpretation:

The relative uncertainty depends on the uncertainty in $pH$, but not on the value of $pH.$

Concept Introduction:

Relative uncertainty:

Compares the size of absolute uncertainty with the size of its associated measurement

  $\text{Relative uncertainty = }\frac{\text{absolute uncertainty}}{\text{magnitude of measurement}}$