Determine the ratio of the mean speed of hydrogen molecules to the mean speed of nitrogen molecules within a sample containing a mixture of the two gases.

Step-by-step solution

The mean speed of gas molecules is given by v = 8RT M , where R is the universal gas constant, T is the absolute temperature, and M is the molar mass of the gas. Since the hydrogen and nitrogen molecules are in the same mixture, they are at the same temperature T . The ratio of the mean speed of hydrogen molecules to that of nitrogen molecules is: v_ H₂ v_ N₂ = M_ N₂ M_ H₂ The molar mass of hydrogen ( H₂ ) is 2 g/mol and the molar mass of nitrogen ( N₂ ) is 28 g/mol . Substituting these values: v_ H₂ v_ N₂ = 28 2 =