Question

Propagation of uncertainty. In an extremely accurate measurement of the Faraday constant, a pure silver anode was oxidized to Ag1 with a constant current of 0.2036390(60.0000004)A for18000.075(60.010s to give a mass loss of4.097900(60.0000003) g from the anode. Given that the atomic mass of Ag is 107.8682 (60.0002), find the value of the Faraday constant and its uncertainty.

Short answer

The Faraday constant is 96500C and the uncertainty will be $96368\pm 0.1369\%$.

Step-by-step solution

Define Faraday's Law of electrolysis

This problem is related to Faraday's Law of electrolysis, states as "mass of substance deposited or discharged is directly proportional to the electricity passed through the cell".

Mathematically given by, $m\infty Q$

Relative uncertainty = ( absolute uncertainty $÷$best estimate )$\times 100\%$

Calculate the faraday’s Laws of electrolysis

According to faraday 1 Faraday (96500C) of current is required to deposit or discharge 1 Equivalent weight of the substance.

Given that

Atomic mass of Ag is 107.868, is also the equivalent weight of silver.

Determination of Faraday Constant

1F = charge on electron $\times$Avogadro number

$$\begin{gathered} 1\mathrm{F}=1.6\times {10}^{-19}\mathrm{C}\times 6.023\times {10}^{23} \\ =96368\mathrm{C} \end{gathered}$$

Therefore 1F = 96368C is the calculated value of the Faraday constant.

Calculate the relative uncertainty

Relative uncertainty = ( absolute uncertainty$÷$best estimate )$\times 100\%$

So from the above:

Relative uncertainty $$\begin{gathered} =\frac{132\times 100}{96368} \\ =0.1369\% \end{gathered}$$

The value can therefore be quoted as role="math" localid="1654772237672" $96368C\pm 0.1369\%$.is the uncertainty. And the Uncertainty value is

$\frac{96368\times 0.1369}{100}\times 132$

And the real Faraday constant will be$96368C\pm 132=96500C$