Question

Q-gas” is a mixture of 98.70% helium and 1.30% butane $\left({\text{C}}_4{\text{H}}_{10}\right)$ by mass. It is used as a filling for gas-flow Geiger counters. Compute the mass percentage of hydrogen in Q-gas.

Short answer

The mass percentage of hydrogen in Q-gas is 16.22%.

Step-by-step solution

Calculation of molar mass of Q-gas

Molar mass of any compound is the fraction of molar mass of the element and the mass percentage of the element, multiplied with 100.

Mass percentage of helium,

${\text{m}}_{\text{He}}\%=98.70\%$

Mass percentage of butane,

Molar mass of helium,

${\text{m}}_{\text{He}}=4.0026{\text{gmol}}^{-1}$

Butane has 4 carbons and 10 hydrogens. So molar mass of butane is calculated by adding the molar mass of 4 carbons and 10 hydrogens.

Molar mass of carbon,

${\text{m}}_{\text{C}}=12.011{\text{gmol}}^{-1}$

Molar mass of hydrogen,

${\text{m}}_{\text{H}}=1.0079{\text{gmol}}^{-1}$

Molar mass of butane,

$\begin{array}{rcl}{\text{M}}_{\text{but}}& =& \left(4\times {\text{m}}_{\text{C}}\right)+\left(\text{10}\times {\text{m}}_{\text{H}}\right)\\ & =& \left(4\times 12.011\right)+\left(\text{10}\times \text{1.0079}\right)\\ & =& 58.123{\text{gmol}}^{-1}\end{array}$

Molar mass of Q-gas,

$\begin{array}{rcl}{\text{M}}_{\text{Q}}& =& {\text{m}}_{\text{He}}+{\text{m}}_{\text{but}}\\ & =& 4.0026+58.12\\ & =& 62.1226{\text{gmol}}^{-1}\end{array}$

Step 2: Mass percentage of hydrogen in Q-gas

Mass percentage of hydrogen in Q-gas can be calculated by dividing the molar mass of hydrogen by molar mass of Q-gas, multiplied by 100.

i.e., Mass percentage of hydrogen in Q-gas,

$\begin{array}{rcl}{\text{m}}_{\text{Q}}\%& =& \frac{{\text{m}}_{\text{H}}}{{\text{M}}_{\text{Q}}}\times 100\\ & =& \frac{\text{10}\times \text{1.0079}}{\text{62.1226}}\times 100\\ & =& 16.22\%\end{array}$

Thus, the mass percentage of hydrogen in Q-gas is 16.22%.