Q42E - Chemistry (OpenStax)

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?

Step-by-Step Solution

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 1: 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.

Step 2: 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:

 

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

 

 

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

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

 

Step 3: 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 \({{\rm{H}}^{\rm{ - }}}\).