Q55E - Chemistry (OpenStax)

Question

What mass of hydrogen gas results from the reaction of 8.5 g of \(KH\) with water?

\(KH{\rm{ }} + {\rm{ }}{H_2}O \to KOH{\rm{ }} + {\rm{ }}{H_2}\)

Step-by-Step Solution

Answer

The mass of the hydrogen gas is \(0.427\;g.\)

Step 1: Definition of molar mass

The molar massof a chemical compound is defined as the massof a sample of a compound divided by the amount of substance in that sample, measured in moles.

Conversion of mass, moles, and volume

Step 2: Molar masses

• Molar mass of \({\rm{K}} = 39,0983\frac{{\rm{g}}}{{{\rm{mol}}}}.\)
• Molar mass of \({\rm{H}} = 1.00784\frac{g}{{\;{\rm{mol}}}}.\)
• Molar mass of \({\rm{KH}} = 40.106\frac{g}{{mol}}.\)
• Molar mass of \({H_2} = 2.016\frac{g}{{mol}}.\)

Step 3: Calculation of mass of hydrogen gas

Since we see from the reaction formula that one mol of \(KH\)gives one mol of \({{\rm{H}}_2}\), we can make a proportion based on the molar masses of the givenmolecules.

 

Molar mass \({\rm{KH}}\) : Molar mass\({H_2}\) = mass \({\rm{KH}}\): mass\({H_2}.\)

 

\(\begin{aligned}{\underline{\phantom{xx}}}{\rm{Mass of }}{{\rm{H}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ Mass of KH}} \times {\rm{Molar mass of }}{{\rm{H}}_{\rm{2}}}}}{{{\rm{ Molar mass of KH }}}}\\ = \frac{{8.5g \times 2.016\frac{g}{{mol}}}}{{40.106\frac{g}{{mol}}}}\\ = 0.427\;{\rm{g}}{\rm{.}}\end{aligned}\)

 

Therefore, the mass of the hydrogen gas is\(0.427g.\)