Place the following 5 gases in order of increasing average molecular speed at 300 K: CO, SF6, H2S, C

Root mean square velocity of gas molecules in an ideal gas is given by:
v_rms = ?( 3? R? T/M)
(R universal gas constant, T absolute temperature, M molar mass of the molecule)


(a)
V_rms is inversely proportional to the square root of the molar mass. That means as lighter the molecules are so greater is v_rms is.

The molar masses of the given gases are
M(CO) = 28.01 g/mol
M(SF?) = 146.06 g/mol
M(H?S) = 34.08g/mol
M(Cl?) = 70.91g/mol
M(HBr) = 80.91g/mol

So the order of these gases in terms of root mean square velocities is:
SF? < HBr < Cl? < H?S < CO


(b)
v_rms = ?( 3 ? 8.3145J/moLK ? 300K / 0.02801 kg/mol) = 516.9 m/s


(c)
v_rms = ?( 3 ? 8.3145J/moLK ? 300K / 0.07091kg/mol) = 324.9 m/s

(1) As average speed of molecules of gases are given v = SQRT(8RT/pi x M), where R is gas constant, T is Temp. in Kelvin, pi = 22/7 or 3.147 and M is molar mass of the gas. Thus, average speed is inversely proportional to the square root of molar mass of the gas.

Now molar masses of CO = 28; SF6 = 146; H2S = 34; Cl2 = 71; HBr = 81
In increasing order molar masses are: CO(28) < H2S(34) < Cl2(71) < HBr(81) < SF6(146)
Therefore, Average speed will be in the order : CO > H2S > Cl2 > HBr > SF6

(2) RMS (Root Mean Square) Speed of the gases = SQRT(3RT/M)
RMS of CO = SQRT ( 3 x 8.314 x 300/28 x 10^-3) = 5.169 x 10^2 m/s (Molar mass in Kg)
RMS of Cl2 = SQRT ( 3 x 8.314 x 300/71 x 10^-3) = 3.246 x 10^2 m/s

(3) Most Probable Speed = SQRT (2RT/M)
OR Most Probable Speed = 0.82 x RMS Speed
Therefore, Most Probable Speed of CO = 0.82 x 5.169 x 10^2 = 4.238 x 10^2 m/s
And Most Probable Speed of Cl2 = 0.82 x 3.246 x 10^2 = 2.66 x 10^2 m/s