Chapter 3, Problem 3.19P

(a)

Interpretation Introduction

Interpretation:

The molecular mass of $\text{NaCl}$ has to be shown as $\text{58}\text{.443}\left(\text{±0}\text{.002}\right)\text{g/mol}\text{.}$.

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

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

For a set measurements having uncertainty values as $e_1,e_2\text{ and }{e}_3$, the uncertainty $(e_4)$ in addition and subtraction can be calculated as follows,

  $e_4=\sqrt{e_1^2+e_2^2+e_3^2}$

Percent relative uncertainty:

  $\text{Percent relative uncertainty = 100 }\times \text{ relative uncertainty}$

(b)

Interpretation Introduction

Interpretation:

The molarity of $\text{NaCl}$ and its uncertainty with an appropriate number of digits has to be expressed.

Concept Introduction:

Number of moles = Molarity $\text{×}$ volume

  $\text{Number of moles}\text{=}\frac{\text{Mass}}{\text{Molar}\text{mass}}$

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

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

For a set measurements having uncertainty values as $e_1,e_2\text{ and }{e}_3$, the uncertainty $(e_4)$ in addition and subtraction can be calculated as follows,

  $e_4=\sqrt{e_1^2+e_2^2+e_3^2}$

Percent relative uncertainty:

  $\text{Percent relative uncertainty = 100 }\times \text{ relative uncertainty}$