Q3.126CP - Chemistry: Molecular Nature Of Matter And Change

Question

A student weighs a sample of carbon on a balance that is accurate to ±0.001 g. (a) How many atoms are in 0.001 g of C? (b) The carbon is used in the following reaction:
$P{b}_3{O}_4\left(s\right)+C\left(s\right)\to 3PbO\left(s\right)+CO\left(g\right)$

What mass difference in the lead(II) oxide would be caused by an error in the carbon mass of 0.001 g?

Step-by-Step Solution

Answer

Answer

1. The number of C atoms in 0.001 g of C is $\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{19}}\mathit{C}\mathit{a}\mathit{t}\mathit{o}\mathit{m}\mathit{s}$

2. The mass difference of PbO is 0.06 g PbO.

Step 1: Calculating the number of C atoms

On multiplying the given mass of C to the molar mass reciprocal and Avogadro’s number.

$$\begin{gathered} \mathit{N}\mathit{o}\mathbf{.}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{C}\mathbf{ }\mathit{a}\mathit{t}\mathit{o}\mathit{m}\mathit{s}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{001}\mathit{g}\mathit{C}\mathbf{\times }\frac{\mathbf{1}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{C}}{\mathbf{12}\mathbf{.}\mathbf{01}\mathbf{g}\mathbf{C}}\mathbf{\times }\frac{\mathbf{6}\mathbf{.}\mathbf{022}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}\mathbf{C}\mathbf{ }\mathbf{a}\mathbf{t}\mathbf{o}\mathbf{m}\mathbf{s}}{\mathbf{1}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{C}} \\ \mathit{N}\mathit{o}\mathbf{.}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{C}\mathbf{ }\mathit{a}\mathit{t}\mathit{o}\mathit{m}\mathit{s}\mathbf{=}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{19}}\mathit{C}\mathbf{ }\mathit{a}\mathit{t}\mathit{o}\mathit{m}\mathit{s} \end{gathered}$$

Step 2: Calculating the mass difference of PbO

The mass difference can be found using,

$$\begin{gathered} \mathit{M}\mathit{a}\mathit{s}\mathit{s}\mathbf{ }\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{P}\mathit{b}\mathit{O}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{001}\mathit{g}\mathit{C}\mathbf{\times }\frac{\mathbf{1}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{C}}{\mathbf{12}\mathbf{.}\mathbf{01}\mathbf{g}\mathbf{C}}\mathbf{\times }\frac{\mathbf{3}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{P}\mathbf{b}\mathbf{O}}{\mathbf{1}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{C}}\mathbf{\times }\frac{\mathbf{223}\mathbf{.}\mathbf{2}\mathbf{g}\mathbf{P}\mathbf{b}\mathbf{O}}{\mathbf{1}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{P}\mathbf{b}\mathbf{O}} \\ \mathit{M}\mathit{a}\mathit{s}\mathit{s}\mathbf{ }\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{P}\mathit{b}\mathit{O}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{06}\mathit{g}\mathit{P}\mathit{b}\mathit{O} \end{gathered}$$