Which of the following gases has the highest average speed at 400K?


NO2

OF2

SO2

SF6

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To determine which gas has the highest average speed at 400K, we can use the kinetic theory of gases. According to this theory, the average speed of a gas molecule is directly proportional to the square root of its temperature.

Let's calculate the average speed for each gas:

1. NO2:
- Temperature: 400K
- Average speed: √(3kT/m), where k is the Boltzmann constant and m is the molar mass of the gas.
- Molar mass of NO2 = 46.01 g/mol
- Average speed of NO2 = √(3 * 1.38 x 10^-23 J/K * 400K / 46.01 g/mol)

2. OF2:
- Temperature: 400K
- Average speed: √(3kT/m), where k is the Boltzmann constant and m is the molar mass of the gas.
- Molar mass of OF2 = 49.00 g/mol
- Average speed of OF2 = √(3 * 1.38 x 10^-23 J/K * 400K / 49.00 g/mol)

3. SO2:
- Temperature: 400K
- Average speed: √(3kT/m), where k is the Boltzmann constant and m is the molar mass of the gas.
- Molar mass of SO2 = 64.06 g/mol
- Average speed of SO2 = √(3 * 1.38 x 10^-23 J/K * 400K / 64.06 g/mol)

4. SF6:
- Temperature: 400K
- Average speed: √(3kT/m), where k is the Boltzmann constant and m is the molar mass of the gas.
- Molar mass of SF6 = 146.06 g/mol
- Average speed of SF6 = √(3 * 1.38 x 10^-23 J/K * 400K / 146.06 g/mol)

Based on these calculations, the gas with the highest average speed at 400K is the gas with the lowest molar mass. So, out of the given options, NO2 has the highest average speed at 400K.

To determine which gas has the highest average speed at 400K, we can use the formula for the root mean square (RMS) speed of a gas molecule:

v = sqrt((3 * k * T) / m)

Where:
- v is the RMS speed
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the gas in kg/mol

To compare the average speeds, we will calculate the RMS speed for each gas at a temperature of 400K and compare the results.

1. NO2 (Nitrogen Dioxide):
- Molar mass: 46.01 g/mol = 0.04601 kg/mol

Using the formula:
v(NO2) = sqrt((3 * 1.38 x 10^-23 J/K * 400 K) / 0.04601 kg/mol)
v(NO2) ≈ 512.89 m/s

2. OF2 (Oxygen Difluoride):
- Molar mass: 49.00 g/mol = 0.04900 kg/mol

Using the formula:
v(OF2) = sqrt((3 * 1.38 x 10^-23 J/K * 400 K) / 0.04900 kg/mol)
v(OF2) ≈ 505.16 m/s

3. SO2 (Sulfur Dioxide):
- Molar mass: 64.06 g/mol = 0.06406 kg/mol

Using the formula:
v(SO2) = sqrt((3 * 1.38 x 10^-23 J/K * 400 K) / 0.06406 kg/mol)
v(SO2) ≈ 484.62 m/s

4. SF6 (Sulfur Hexafluoride):
- Molar mass: 146.06 g/mol = 0.14606 kg/mol

Using the formula:
v(SF6) = sqrt((3 * 1.38 x 10^-23 J/K * 400 K) / 0.14606 kg/mol)
v(SF6) ≈ 354.62 m/s

Comparing the calculated RMS speeds, we find that NO2 has the highest average speed at 400K with a value of approximately 512.89 m/s.