Question

A hydride of silicon prepared by the reaction of \({\rm{M}}{{\rm{g}}_2}{\rm{Si}}\) with acid exerted a pressure of 306 torr at \({26^\circ }{\rm{C}}v\)in a bulb with a volume of\(57.0\;{\rm{mL}}\). If the mass of the hydride was\(0.0861\;{\rm{g}}\), what is its molecular mass? What is the molecular formula for the hydride?

Short answer

The molecular mass of \(M\;({\rm{hydride}})\)is \(92.1\;{\rm{g}}/{\rm{mol}}\).The molecular formula of hydride is \({{\rm{H}}^{\rm{ - }}}.\)

Step-by-step solution

Definition of molecular mass

The mass of a patch is measured in Daltons and is called a molecular mass (m). Because some compounds contain colorful isotopes of an element, different motes of the same substance may have different molecular weights.

Calculate the molecular mass of the hydride

Using the ideal gas law, we can calculate the number of moles of hydride.

\({\rm{Number of moles = }}\frac{{{\rm{Pressure \times Volume}}}}{{{\rm{Gas constant \times Temperature}}}}.\)

Put the known values as shown below:

\(\begin{aligned}{}n({\rm{ hydride }}) = \frac{{306{\rm{ torr }} \times \frac{{133.322Pa}}{{1torr}} \times 5.7 \times {{10}^{ - 5}}{m^3}}}{{8.314\frac{J}{{Kmol}} \times 299K}}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = 9.35 \times {10^{ - 4}}\;{\rm{mol}}{\rm{.}}\end{aligned}\)

With the mass and the number of moles known, we can calculate the molecular mass of the hydride.

\(\begin{aligned}{}{\rm{Given mass(m) = Number of moles(n) \times Molar mass(M)}} \to {\rm{M = }}\frac{{\rm{m}}}{{\rm{n}}}\\{\rm{M(hydride) = }}\frac{{{\rm{0}}{\rm{.0861g}}}}{{{\rm{9}}{\rm{.35 \times 1}}{{\rm{0}}^{{\rm{ - 4}}}}{\rm{\;mol}}}}\\{\rm{ = 92}}{\rm{.1g/mol}}{\rm{.}}\end{aligned}\)

Molecular formula of hydride

Hydride is the anion of a hydrogen atom and so it contains a negative charge. Thus, the molecularformula of hydride is \({{\rm{H}}^{\rm{ - }}}\).