Questions: 1. Five identical balloons are shown below. Each is filled to the same volume with the pure gases indicated in the diagram at 0°C and 1.0 atm pressure (STP). a. Which balloon contains the greatest mass of gas? Explain. b. Compare the average kinetic energies of the gas molecules in the balloons. Explain.

1. Five identical balloons are shown below. Each is filled to the same volume with the pure gases indicated in the diagram at 0°C and 1.0 atm pressure (STP). a. Which balloon contains the greatest mass of gas? Explain. b. Compare the average kinetic energies of the gas molecules in the balloons. Explain.
Transcript text: 1. Five identical balloons are shown below. Each is filled to the same volume with the pure gases indicated in the diagram at $0^{\circ} \mathrm{C}$ and 1.0 atm pressure (STP). a. Which balloon contains the greatest mass of gas? Explain. b. Compare the average kinetic energies of the gas molecules in the balloons. Explain.
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Solution

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Solution Steps

Step 1: Identify the conditions and gases

The problem states that five identical balloons are filled with different gases (O₂, CO₂, He, CH₄, N₂) at the same volume, temperature (0°C), and pressure (1.0 atm).

Step 2: Use the Ideal Gas Law

Since the conditions are the same for all gases, we can use the Ideal Gas Law (PV = nRT) to determine the number of moles (n) of each gas. Given that volume (V), temperature (T), and pressure (P) are constant, the number of moles (n) will be the same for each gas.

Step 3: Calculate the molar masses

Determine the molar masses of each gas:

  • O₂: 32 g/mol
  • CO₂: 44 g/mol
  • He: 4 g/mol
  • CH₄: 16 g/mol
  • N₂: 28 g/mol
Step 4: Determine the mass of gas in each balloon

Since the number of moles (n) is the same for each gas, the mass of gas in each balloon is directly proportional to its molar mass. The balloon with the greatest molar mass will contain the greatest mass of gas.

Final Answer

The CO₂ balloon contains the greatest mass of gas because CO₂ has the highest molar mass (44 g/mol) among the gases listed.

Step 1: Understand kinetic energy dependence

The average kinetic energy of gas molecules depends on temperature, not on the type of gas. At the same temperature, all gases have the same average kinetic energy.

Step 2: Apply the kinetic theory of gases

According to the kinetic theory of gases, the average kinetic energy of gas molecules is given by (3/2)kT, where k is the Boltzmann constant and T is the temperature.

Final Answer

The average kinetic energies of the gas molecules in all the balloons are the same because they are all at the same temperature (0°C).

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