Final answer:
At 25 °C, the gases arranged from the lowest to the highest average molecular speed are CO₂, O₂, N₂, and He, as molecular speed is inversely related to the square root of the gas's molar mass.
Step-by-step explanation:
To arrange the following gases in order of increasing average molecular speed at 25 °C (He, O₂, CO₂, N₂), we must consider Graham's law of effusion which states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass. In this context, molecular speed is also inversely related to the square root of molar mass. Therefore, a gas with a lower molar mass will have a higher average molecular speed at a given temperature.
The molar masses of the gases given are: He (4 g/mol), N₂ (28 g/mol), O₂ (32 g/mol), and CO₂ (44 g/mol). Arranging these gases by their molar masses, we can infer the order of their molecular speeds. The gas with the lowest molar mass will have the highest molecular speed, and the gas with the highest molar mass will have the lowest speed.
Therefore, at 25 °C, the gases arranged in order of increasing average molecular speed is: CO₂, O₂, N₂, He.