Calculate the root mean square speed ofmethave molecules at 27 degree Celsius
Answers
Answer:
Answer: The root mean square speed is, 683.8m/s683.8m/s
Explanation:
The formula used for root mean square speed is:
\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}ν
rms
=
M
3kN
A
T
where,
\nu_{rms}ν
rms
= root mean square speed
k = Boltzmann’s constant = 1.38\times 10^{-23}J/K1.38×10
−23
J/K
T = temperature = 27^0C=(27+273)=300 K27
0
C=(27+273)=300K
M = atomic mass of methane = 16g/mol
N_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/mol
3×(1.38×10
−23
J/K)×(6.02×10
23
mol
−1
)×(300K)
\nu_{rms}=683.8m/sν
rms
=683.8m/s
The root mean square speed is, 683.8m/s683.8m/s