Question

Which of the following gases has the lowest average speed at 25?

NH2NH2

C2H4

He

N2

Answer 1

a) Average speed of a gas molecule, Vavg = 8RT/M

For all the gas molecules Ideal gas constant, R and Temperature, T remains constant i.e. 25 C but molar mass of gas molecules differ.

Hence average speed of gas molecule depends upon molar mass of a gas molecule i.e. inversely proportional to the molar mass of gas molecules.

NH₂NH₂ : Molar mass of hydrazine = 32.05 g/mol

C₂H₄ : Molar mass of ethane = 28.05 g/mol

He : Molar mass of helium = 4 g/mol

N₂ : Molar mass of nitrogen = 28 g/mol

As average speed of gas molecule is inversely related to the molar mass of gas molecule.

The gas molecule with lowest average speed at 25 C should have higher molar mass. From the above gaseous molecules, the one with highest molar mass is hydrazine (NH₂NH₂).

or Vavg can be calculated for all the gases and can be cross checked.

NH₂NH₂ : Molar mass of hydrazine = 32.05 g/mol , Vavg = 8 x 8.314 J/mol K x 298 Kx1000/3.14 x32.05 kg/mol =

19820.576x1000/3.14x32.05 = 19820576/100.637 = 196951.2 = 443.79 m/s

C₂H₄ : Molar mass of ethane = 28.05 g/mol = 8 x 8.314 J/mol K x 298 Kx 1000/3.14 x28.05 kg/mol = 19820576/88.077 = 225036.91 = 474.38 m/s

He : Molar mass of helium = 4 g/mol = 8 x 8.314 J/mol K x 298 Kx1000/3.14x4 g/mol = 19820576/12.56 = 1578071.34 = 1256.2 m/s

N₂ : Molar mass of nitrogen = 28 g/mol = 8 x 8.314 J/mol K x 298 Kx1000/.14 x 28 g/mol = 19820576/87.92 = 225438.76 = 474.80 m/s

From the above 4 gases hydrazine (NH₂NH₂) have lowest average speed