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Which one of the following is the kinetic energy of a gaseous mixture containing $3 \mathrm{~g}$ of hydrogen and $80 \mathrm{~g}$ of oxygen at temperature $T(K)$ ?
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Verified Answer
The correct answer is:
$6RT$
Number of moles of hydrogen
$=\frac{3 g}{2 g \mathrm{~mol}^{-1}}=1.5$
Number of moles of oxygen
$=\frac{80 \mathrm{~g}}{32 \mathrm{~g} \mathrm{~mol}^{-1}}=2.5=2.5$
Total number of moles in gaseous mixture of hydrogen and oxygen,
$\begin{aligned}
& n=1.5+2.5=4 \\
& \mathrm{KE}=\frac{3}{2} n R T=\frac{3}{2} \times 4 \times R T=6 R T
\end{aligned}$
$=\frac{3 g}{2 g \mathrm{~mol}^{-1}}=1.5$
Number of moles of oxygen
$=\frac{80 \mathrm{~g}}{32 \mathrm{~g} \mathrm{~mol}^{-1}}=2.5=2.5$
Total number of moles in gaseous mixture of hydrogen and oxygen,
$\begin{aligned}
& n=1.5+2.5=4 \\
& \mathrm{KE}=\frac{3}{2} n R T=\frac{3}{2} \times 4 \times R T=6 R T
\end{aligned}$
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