If He gas has an average kinetic energy of 8970 J/mol under certain conditions,
ID: 608964 • Letter: I
Question
If He gas has an average kinetic energy of 8970 J/mol under certain conditions, what is the root mean square speed of Cl2 gas molecules under the same conditions? answer in m/sExplanation / Answer
Under the same conditions, the relative rates of diffusion of two gases can be determined by the ratio of their average speeds (or "root-mean-square speeds") : r1/r2 = sqrt (m2/m1) where r = rate of effusion for given gas with a molecular weight, m. Therefore, for comparison between rates of effusion of F2 vs Rn where r1&m1 refer to F2 and r2&m2 to Rn: r1/r2 = sqrt (222/39) = 2.386 --> thus, r1 = rate of effusion of F2 is about 2.39 times faster than the rate of effusion of Rn. In short, the rate of effusion of a gas is inversely proportional to the square root of its molecular weight. The above relationship holds true for comparing the rates of effusion of two gases of differing molecular weights ONLY when the temperature and pressure is held constant. In order to calculate the root-mean-square (rms) speed of a specific gas at a specific temperature and pressure, you must use a different equation: The root-mean-square speed for a gas (units: meters/second) is equal to the sqrrt(3RT/M) where: T = temperature in Kelvins = degrees Celsius + 273 M = Molecular Weight = kg/mol R = Ideal gas constant = 8.314 J/mol K = 8.314 kg m2/s2 mol K You should be able to use this equation to solve for the rms speed of chlorine gas at room temp. *By the way, usually room temperature is defined to be 25 degrees C rather than 20. Nonetheless, the above equation will work for either temperature as long as you convert to Kelvins. *Also, chlorine gas exists as a diatomic gas, Cl2 thus M=70g/mol = 0.07kg/mol Hope this helps! Check out the sites below for further explanation.