Calculate root mean square of methane molecule at 270C.

1.	Calculate root mean square of methane molecule at 270C.
Answer» tion:The root mean square speed is, 683.8m/s683.8m/sExplanation:The FORMULA used for root mean square speed is:\nu_{rms}=\SQRT{\frac{3kN_AT}{M}}ν rms = M3kN A T where,\nu_{rms}ν rms = root mean square speedk = Boltzmann’s CONSTANT = 1.38\times 10^{-23}J/K1.38×10 −23 J/KT = temperature = 27^0C=(27+273)=300 K27 0 C=(27+273)=300KM = atomic mass of methane = 16g/molN_AN A = AVOGADRO’s number = 6.02\times 10^{23}mol^{-1}6.02×10 23 mol −1 Now put all the given values in the above root mean square speed formula, we get:\nu_{rms}=\sqrt{\frac{3\times (1.38\times 10^{-23}J/K)\times (6.02\times 10^{23}mol^{-1})\times (300K)}{16\times 10^{-3}kg/mol}}ν rms = 16×10 −3 kg/mol3×(1.38×10 −23 J/K)×(6.02×10 23 mol −1 )×(300K) \nu_{rms}=683.8m/sν rms =683.8m/sThe root mean square speed is, 683.8m/s683.8m/s

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