Final answer:
At 25°C, CH₄ (methane) has the greatest average molecular speed among the given gas samples due to its lowest molar mass.
Step-by-step explanation:
The student question pertains to identifying which of the given gas samples - Kr, CH₄, N₂, CH₂Cl₂, CO₂ - would have the greatest average molecular speed at 25°C. The average molecular speed of a gas at a constant temperature is inversely proportional to the square root of the molar mass (M) of the gas molecules, as stated by Graham's law. This is represented by the equation u ≈ 1/√M, where u is the average speed.
The molar masses of the given gases are as follows: Kr (83.80 g/mol), CH₄ (16.04 g/mol), N₂ (28.02 g/mol), CH₂Cl₂ (84.93 g/mol), CO₂ (44.01 g/mol). Given these masses, CH₄, methane, has the lowest molar mass and therefore, according to the formula, it will have the highest average molecular speed at the given temperature.