Determine the molar mass of each of the following compounds, all of which have been used as explosives: (a) lead azide, PbN6, (b) nitroglycerin, C3H5N3O9, (c) mercury fulminate, Hg(ONC)2

Question

Determine the molar mass of each of the following compounds, all of which have been used as explosives: (a) lead azide, [latex]PbN_{6}[/latex], (b) nitroglycerin, [latex]C_{3}H_{5}N_{3}O_{9}[/latex], (c) mercury fulminate, [latex]Hg(ONC)_{2}[/latex]

Strategy
We must determine the mass contributed by each element and then add them up to calculate the molar mass. When parentheses appear in the formula, each atom inside the parentheses must be multiplied by its own subscript and by the subscript appearing after the right-hand parenthesis.

Accepted Answer

[latex] \begin{matrix}(a) \ PbN_{6}: & & 1 \ mole \ Pb: & 1 × 207.2 \ \ \ g/mol \ = \ \ \ \ 207.2 \ \ \ g/mol \ && 6 \ mole \ N: & \ \ \ 6 × 14.0067 \ \ \ g/mol \ = \ \ \ \ \underline{84.042 \ \ \ g/mol} \ & && \qquad \quad Molar \ mass = \quad291.2 \ g/mol \end{matrix}[/latex]

[latex] \begin{matrix} (b) \ C_{3}H_{5}N_{3}O_{9}: & 3 \ moles \ C: \ 3 imes 12.011 \ g/mol=36.033 \ g/mol \ & 5 \ moles \ H: \ 5 imes 1.0079 \ g/mol=5.0395 \ g/ml \ & 3 \ moles \ N: \ 3 imes 14.0067 \ g/mol=42.0202 \ g/ml \ & 9 \ moles \ O: \ 9 imes 15.9994 \ g/mol=\underline{143.995 \ g/mol} \ & \qquad \quad \quad \quad Molar \ mass \quad\quad = 227.087 \ g/mol \end{matrix}[/latex]

[latex] \begin{matrix} (c) \ Hg(ONC)_{2}: & \ 1 \ mole \ Hg: \ 1 imes 200.59 \ g/mol=200.59 \ g/mol \ & 2 \ moles \ O: \ 2 imes 15.9994 \ g/mol=31.9988 \ g/mol \ & 2 \ moles \ N: \ 2 imes 14.0067 \ g/mol=28.0134 \ g/mol \ & 2 \ moles \ C: \ 2 imes 12.011 \ g/mol=\underline{24.022 \ g/mol} \ & \quad\quad\quad\quad \quad Molar \ mass \quad\quad 284.62 \ g/mol\end{matrix}[/latex]

Analyze Your Answer
Looking at these three compounds, we see that nitroglycerin has the smallest molar mass even though it clearly contains the most atoms per molecule. Does this make sense? The key factor is that both lead azide and mercury fulminate contain elements with large molar masses, so it is not surprising that nitroglycerin is the least massive of these three molecules.

Discussion
The number of significant figures to which the molar masses of the elements are known varies from one element to another, as you can see if you examine the periodic table inside the front cover of this book. So the appropriate number of significant figures in the molar masses here varies according to the elements in each molecule.

Question 3.EP.5: Determine the molar mass of each of the following compounds,...

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