Question

Calculate the kinetic energy (in joule) for $8.00\text{g}$ of methane at ${27}^{\circ }\text{C}$.

Answer 1

Number of gram moles of methane $=\frac{Mass}{Molarmass}=\frac{8}{16}=\frac{1}{2}$
Temperature of gas $\left(T\right)=27+273=300\text{K}$
$R=8.32{\text{J K}}^{-1}{\text{mol}}^{-1}$
Kinetic energy for one mole $=\frac{3}{2}RT$
$=\frac{3}{2}\times 8.314\times 300\text{J}/mol$
Thus,
Kinetic energy for $\frac{1}{2}$ gram mole $=\frac{1}{2}\times \frac{3}{2}\times 8.314\times 300=1870.65\text{J}$