A 3.0 L container of nitrogen gas (N2) and a 5.0 L container of oxygen gas (O2) are both at 20^∘

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A 3.0 L container of nitrogen gas (N2) and a 5.0 L container...

A $3.0 \mathrm{L}$ container of nitrogen gas $\left(\mathrm{N}_{2}\right)$ and a $5.0 \mathrm{L}$ container of oxygen gas $\left(\mathrm{O}_{2}\right)$ are both at $20^{\circ} \mathrm{C}$ and 1.0 atm. (a) Which gas has the larger rms speed? Explain. (b) At what temperature will oxygen gas have the same rms speed as nitrogen when the nitrogen is at $20^{\circ} \mathrm{C} ?(\mathrm{c})$ How much heat must flow into or out of the container of oxygen to change its temperature from $20^{\circ} \mathrm{C}$ to the temperature you found in part (b)?

A $3.0 \mathrm{L}$ container of nitrogen gas $\left(\mathrm{N}_{2}\right)$ and a $5.0 \mathrm{L}$ container of oxygen gas $\left(\mathrm{O}_{2}\right)$ are both at $20^{\circ} \mathrm{C}$ and 1.0 atm. (a) Which gas has the larger rms speed? Explain.
(b) At what temperature will oxygen gas have the same rms speed as nitrogen when the nitrogen is at $20^{\circ} \mathrm{C} ?(\mathrm{c})$ How much heat must flow into or out of the container of oxygen to change its temperature from $20^{\circ} \mathrm{C}$ to the temperature you found in part (b)?

Key Concepts

Root Mean Square (rms) Speed

Root mean square speed is a statistical measure of the speed of gas molecules derived from kinetic theory. It is given by the formula urms = ?(3RT/M), which shows that for a given temperature, lighter molecules (with a lower molar mass) will have a higher rms speed than heavier molecules.

Kinetic Molecular Theory

Kinetic molecular theory explains the behavior of gases by modeling them as a large number of small particles in constant, random motion. This theory underpins macroscopic gas laws and shows how molecular mass and temperature determine molecular speeds, collision rates, and energy distribution.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. It is essential for determining the state of a gaseous system and links these macroscopic properties to molecular behavior, which influences calculations such as rms speed.

Heat Transfer and Specific Heat Capacity

Heat transfer into or out of a gas is calculated using its specific heat capacity, which quantifies the amount of heat required to change the temperature of a unit mass of the gas by one degree. For changes in temperature at constant volume or pressure, understanding the specific heat capacity is crucial to determine the heat exchange associated with altering molecular speeds and internal energy.

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