Two identical 732.0-L tanks each contain 212.0 g of gas at 293 K, with neon in one tank and nitrogen in the other. Based on the assumptions of kinetic–molecular theory, rank the gases from low to high for each of the following properties. (a) Average speed
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Determine the molar mass of each gas: Neon (Ne) has a molar mass of approximately 20.18 g/mol, and Nitrogen (N2) has a molar mass of approximately 28.02 g/mol.
Use the formula for average speed (root-mean-square speed) of a gas: \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass in kg/mol.
Since both gases are at the same temperature and the same conditions, the average speed depends inversely on the square root of the molar mass.
Compare the molar masses: Neon has a lower molar mass than Nitrogen, which means Neon atoms will have a higher average speed than Nitrogen molecules.
Rank the gases based on average speed from low to high: Nitrogen (N2) will have a lower average speed than Neon (Ne).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Kinetic Molecular Theory
Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that gas particles are far apart, move freely, and collide elastically. This theory helps in understanding how temperature and mass affect the speed of gas particles, which is crucial for comparing the average speeds of different gases.
The average speed of gas molecules is influenced by their temperature and molar mass. According to the equation for root mean square speed, lighter gases (lower molar mass) move faster than heavier gases at the same temperature. This concept is essential for ranking the average speeds of neon and nitrogen in the given scenario.
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. It plays a critical role in determining the average speed of gas molecules, as lighter gases have higher average speeds compared to heavier gases at the same temperature. Understanding the molar masses of neon and nitrogen is key to solving the ranking problem.
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