Answer : The root-mean-square speed of methane gas is, 739.7 m/s
Solution :
Formula used :
[tex]v_{rms}=\sqrt{\frac{3RT}{M}}[/tex]
where,
[tex]v_{rms}[/tex] = root mean square speed
R = gas constant = [tex]8.314\text{ Kg }m^2s^{-2}K^{-1}mole^{-1}[/tex]
T = temperature of gas = [tex]78^oC=78+273=351K[/tex]
M = molecular weight of methane = 16 g/mole = 0.016 Kg/mole (1 Kg = 1000 g)
Now put all the given values in the above formula, we get the rms speed.
[tex]v_{rms}=\sqrt{\frac{3\times (8.314\text{ Kg }m^2s^{-2}K^{-1}mole^{-1})\times (351K)}{(0.016Kg/mole)}}=739.7m/s[/tex]
Therefore, the root-mean-square speed of methane gas is, 739.7 m/s
