Question

Calculate the root-mean-square speed of methane, ch4 (g), at 78°c. root mean square speed = u = [3rt/(molar mass) ] ^ (1/2) think about which r you are going to use and make sure to show the units!

Answer 1

Answer : The root-mean-square speed of methane gas is, 739.7 m/s

Solution :

Formula used :

$v_{rms}=\sqrt{\frac{3RT}{M}}$

where,

$v_{rms}$ = root mean square speed

R = gas constant = $8.314\text{ Kg }m^2s^{-2}K^{-1}mole^{-1}$

T = temperature of gas = $78^oC=78+273=351K$

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.

$v_{rms}=\sqrt{\frac{3\times (8.314\text{ Kg }m^2s^{-2}K^{-1}mole^{-1})\times (351K)}{(0.016Kg/mole)}}=739.7m/s$

Therefore, the root-mean-square speed of methane gas is, 739.7 m/s

Answer 2

Rms speed u = √ 3RT/MT = 78 + 273 =351 K(Absolute temperature)R = 8.314J/K.molM = molar mass of CH4= 16.05*10⁻³ kg/mol
so the value of u = 738.6 m / s