WF6 is one of the heaviest known gases. How much slower is the root-mean-square speed of WF6 than He at 300 K?

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Identify the formula for root-mean-square speed: \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass in kg/mol.

Calculate the molar mass of \( \text{WF}_6 \) and \( \text{He} \). For \( \text{WF}_6 \), add the atomic mass of tungsten (W) and six times the atomic mass of fluorine (F). For \( \text{He} \), use the atomic mass of helium.

Convert the molar masses from g/mol to kg/mol by dividing by 1000.

Use the root-mean-square speed formula to find the \( v_{rms} \) for both \( \text{WF}_6 \) and \( \text{He} \) at 300 K.

Calculate the ratio of the \( v_{rms} \) of \( \text{He} \) to \( \text{WF}_6 \) to determine how much slower \( \text{WF}_6 \) is compared to \( \text{He} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Root-Mean-Square Speed

Root-mean-square speed (rms speed) is a measure of the average speed of gas molecules in a sample. It is calculated using the formula v_rms = sqrt(3RT/M), where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. This concept is crucial for comparing the speeds of different gases at the same temperature.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It directly influences the root-mean-square speed of a gas; heavier gases have higher molar masses, resulting in slower rms speeds at a given temperature. Understanding molar mass is essential for calculating and comparing the speeds of different gases.

Kinetic Molecular Theory

Kinetic molecular theory explains the behavior of gases in terms of particles in constant motion. It posits that the temperature of a gas is proportional to the average kinetic energy of its molecules. This theory helps in understanding how temperature and molar mass affect the speed of gas molecules, which is fundamental for solving the given question.

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Kinetic Molecular Theory

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The temperature of a 5.00-L container of N2 gas is increased from 20 °C to 250 °C. If the volume is held constant, predict qualitatively how this change affects the following: (a) the average kinetic energy of the molecules.

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