A sealed container holds 10 g of an ideal gas X at 300 K, exerting a pressure of 2 atm. When 80 g of a different ideal gas Y is introduced at the same temperature, the pressure rises to 6 atm. What is the ratio of the root mean square speeds of X and Y at 300 K?

Question

Accepted Answer

2: 1. The ratio of the root mean square speeds of X and Y at 300 K is 2: 1 because the root mean square speed of an ideal gas is given by vₚ = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass, and since the temperature is the same for both gases, the ratio of their root mean square speeds is equal to the inverse ratio of the square roots of their molar masses.

A sealed container holds 10 g of an ideal gas X at 300 K, exerting a pressure of 2 atm. When 80 g of a different ideal gas Y is introduced at the same temperature, the pressure rises to 6 atm. What is the ratio of the root mean square speeds of X and Y at 300 K?

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