Question

The lead(IV) oxide used in car batteries is prepared by coating the electrode plate with PbO and then oxidizing it to lead dioxide (${\mathbf{\text{PbO}}}_{\mathbf{\text{2}}}$). Despite its name,${\mathbf{\text{PbO}}}_{\mathbf{\text{2}}}$has a nonstoichiometric ratio of lead to oxygen of about. In fact, the holes in the${\mathbf{\text{PbO}}}_{\mathbf{\text{2}}}$crystal structure due to missing O atoms are responsible for the oxide’s conductivity. (a) What is the mole % of O missing from the${\mathbf{\text{PbO}}}_{\mathbf{\text{2}}}$structure? (b) What is the molar mass of the nonstoichiometric compound?

Short answer

a) The mole % is obtained as:$1\%$ .

b) The molar mass of nonstoichiometric compound is obtained as: ${\text{238.88 g mol}}^{\text{- 1}}$.

Step-by-step solution

Evaluating the mole %

a) ${\text{PbO}}_{\text{2}}$has two moles of oxygen per mole. ${\text{PbO}}_{1.98}$has $1.98$moles of oxygen per mole.

The difference between the two sums may be calculated as follows:

data-custom-editor="chemistry" $$\begin{gathered} {\text{n(O)}}_{\text{missing=}}\text{2.0mol-1.98mol} \\ {\text{n(O)}}_{\text{missing}}\text{=0.02mol} \\ \%\text{(O)=}\frac{\mathrm{n}{\left(\mathrm{O}\right)}_{\mathrm{missing}}}{{\displaystyle \text{n}\left({\text{O}}_{\text{PbO}}^{\text{2}}\right)}}\text{×100\%} \\ \%{\text{(O)}}_{\text{missing=}\frac{0.02\mathrm{mol}}{2.0\mathrm{mol}}\text{×100\%}} \\ \%{\text{(O)}}_{\text{missing=1\%}} \end{gathered}$$

Therefore, the mole % is $1\%$: .

Evaluating the molar mass

b) Using data from the periodic table of elements, the molar mass of the nonstoichiometric compound may be calculated:

$$\begin{gathered} \text{M}\left({\text{PbO}}_{\text{1.98}}\right)\text{=A}\left(Pb\right)\text{+1.98×A}\left(O\right) \\ \text{M}\left({\text{PbO}}_{\text{1.98}}\right){\text{=207.2gmol}}^{-1}\text{+1.98×15.999}{\mathrm{gmol}}^{-1} \\ \text{M}\left({\text{PbO}}_{\text{1.98}}\right)\text{=238.88}{\mathrm{gmol}}^{-1} \end{gathered}$$

Therefore, the molar mass is: $238.88{\mathrm{gmol}}^{-1}$.