Question

Arrange the following molecules in order of increasing average molecular speed.

NO2 at 327K, He at 443K, He at 386K, O2 at 386K

Enter formulas and temperatures in the boxes below: 1 = slowest, 4 = fastest

Answer 1

The Average molecular speed is defined as the square root of the ratio of products of three times the Gas constant and Temperature to the molar mass of the gas molecule.

Where, the term average means not a single molecule and refers to a collection of molecules that are independent.

The average molecular speed (C) is defined as -

where,

R = 8.314 J/K/mol but since we require speed (in m/s) so we break down the units and express in terms of Kg so that finally we are left with the unit of speed which is m/s

i.e. R = 8.314 Kg m² s^-2mol^-1 K^-1

T = Temperature in Kelvin , K

M = Molar mass . It has the unit of g mol ^-1 but since R has Kg in its unit so we express M in terms of Kg mol ^-1

Unit Cancellations-

The units cancellation shows us how are we left with m/s

K^-1 and K gets cancelled ; Kg and Kg gets cancelled ; mol ^-1 and mol gets cancelled and we are left with

Since means anything raised to the power 1/2 so,

or,

Now, let us solve the Average molecular speeds for the above mentioned gases-

• NO₂ at 327 K

The Molecular mass M of NO₂is 0.0460055 kg/mol

Using the above formula-

• He at 443 K

The molecular mass of He in Kg/mol is = 0.004002602 kg/mol

• He at 386 K

The molecular mass of He in Kg/mol is = 0.004002602 kg/mol

• O₂ at 386 K

The Molecular mass of O₂ in Kg/mol is = 0.031998 Kg/mol

Thus , the order of increasing average molecular speed is-

(1 slowest ; 4 = fastest)

1. 
2. 
3. 
4.