Suppose you weigh three samples of AgCl precipitate using the exact mass weighing method. The...

Part (a.)

First, we have to calculate the average ({eq}\rm \chi {/eq}) of the measurements by adding up all the measurements (x) and dividing the sum by the number of samples (n).

Average of Measurements:

{eq}\rm \chi = \dfrac {x_1 + x_2 + x_3}{n}\\ \chi = \dfrac {0.2496~g + 0.2502~g + 0.2498~g}{3}\\ \chi = \dfrac {0.7496~g}{3}\\ \chi = 0.2499~g {/eq}

The standard deviation (SD) of a measurement depends on the measurements, the average, and the number of samples in the population.

Standard Deviation:

{eq}\rm SD = \sqrt{ \dfrac {\Sigma (x - \chi)^2}{n - 1}}\\ SD = \sqrt{ \dfrac {(0.2496 - 0.2499)^2 + (0.2502 - 0.2499)^2 + (0.2498 - 0.2499)^2}{3 - 1}}\\ SD = \sqrt{ \dfrac {(-0.0003)^2 + (0.0003)^2 + (-0.0001)}{2}}\\ SD = \sqrt{ \dfrac {9 \times 10^{-8} + 9 \times 10^{-8} + 1 \times 10^{-8}}{2}}\\ SD = \sqrt{ \dfrac {19 \times 10^{-8}}{2}}\\ \boxed{\mathbf{ SD = 9.5 \times 10^{-8}}} {/eq}

Part (b.)

Relative standard deviation (RSD) is the product of dividing the standard deviation by the mean multiplied by 100%.

Relative Standard Deviation:

{eq}\rm RSD = \dfrac {SD}{\chi} \cdot 100\%\\ RSD = \dfrac {9.5 \times 10^{-8}}{0.2499} \cdot 100\%\\ RSD = 3.8 \times 10^{-7} \cdot 100\%\\ \boxed{\mathbf{ RSD = 3.8 \times 10^{-5}\%}} {/eq}