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4. What is the rms speed of an nitrogen molecules contained in an `8.5`-`m^3` volume at `2.1\ atm` if the total amount of nitrogen is `1300 mol`?
4. What is the rms speed of an nitrogen molecules contained in an 8.5-m^3 volume at 2.1\ atm if the total amount of nitrogen is 1300 mol? `PV = NkT`
`v_(rms) = sqrt((3kT)/m)`
`v_(rms)= 3.9 times 10^2\ m//s`
Given:
`V = 8.5\ m^3`
`P = 2.1\ atm = 2.1 times 1.013 times 10^5\ Pa`
`n = 1300\ mol`
`N = 1300 times 6.02 times 10^23` molecules
Known:
`k = 1.38 times 10^(-23)\ J/K`
`m_N_2 = 28\ u = 28 times 1.66 times 10^(-27)\ kg`
Solution
`PV = NkT => T = (PV)/(Nk)`
`v_(rms) = sqrt((3kT)/m) = sqrt((3k((PV)/(Nk)))/m) = sqrt((3PV)/(Nm))`
`v_(rms)=sqrt((3(2.1 times 1.013 times 10^5\ Pa)(8.5\ m^3))/((1300 times 6.02 times 10^23)(28 times 1.66 times 10^(-27)\ kg)))`
`v_(rms)= 3.9 times 10^2\ m//s` |