Answer:
M = 613.8455 kg/mol
Explanation:
RMS velocity or root mean square velocity has a formula for particles:
RMS = (3*R*T/ M)^ (1/2)
Where R is the ideal gas constant = 8.314 (kg*m^2 / s^2)/ K*mol
T is the temperature in Kelvin
M is the mass of a mole of the gas in kilograms (kg)
1) Convert the temperature to Kelvin for the N2 particles
T = *C +273
T = 50 + 273
T = 323 K
2) Find the molar mass of the particles in kg for N2
using the periodic table: Nitrogen (N) molar mass is 14.00667 g/mol
N2 molar mass = 2 * 14.00667 = 28.01334 g/mol
Convert to kg/mol using dimensional analysis and conversion factor of 1 kg = 1000 g
28.01334 g / mol * 1 kg / 1000 g = 0.02801334 kg/mol
4) find the RMS of N2
RMS = (3 * (8.314 (kg*m^2 / s^2)/K*mol) * (323K) / 0.02801334 kg/mol))^1/2
=536.2712 m/s
5)If we take 0.5 of N2 RMS or 1/2 we get: 268.1356 m/s for the RMS of the unknown gas
6) Rearrange the equation to solve for M
RMS=(3RT/M)^1/2
Solve for M
We know that a^(1/2) = sqrt(a)
sqrt(RMS) = (3RT/M)
sqrt(RMS) * M = 3RT
M = 3RT / sqrt(RMS)
5) Change the temperature to Kelvins
T = 130 +273 = 403 K
6) Plug the numbers in and solve for M
M = (3*(8.314 (kg*m^2 / s^2)/K*mol) * (403 K)) / sqrt(268.1356 m/s)
M = 613.8455 kg/mol
