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Root mean square velocity is the square root of the mean of the squares of speeds of different molecules. From kinetic theory of gas, the formula of root mean square velocity=C= √
=√
=√
, where, R= Universal gas constant, T= Absolute temperature, P= Pressure, V= Volume of gas, d= Density of gas.
Given, T=273 K, P=1.00 x 10⁻² atm, d=1.24 x 10⁻⁵ g/cm³.
(a) Using the formula =√
=√(3X1.00X10⁻²)/(1.24X10⁻⁵)=49.18
(b) Molar mass can be determined by using the formula =√{3RT}{M}
49.18=√
49.18²=√(3X8.314X273)/M
M=
M=1.67 ≅ 2
Molecular mass is 2.
(c) The gas is Helium (He) whose molecular mass is 2.