Which has a higher average speed, H2 at 150 K or He at 375 °C?

검증된 단계별 안내

Convert the temperature of helium from Celsius to Kelvin by using the formula: \( T(K) = T(°C) + 273.15 \).

Use the formula for average speed of a gas, which is given by the equation: \( v_{rms} = \sqrt{\frac{3kT}{m}} \), where \( v_{rms} \) is the root mean square speed, \( k \) is the Boltzmann constant, \( T \) is the temperature in Kelvin, and \( m \) is the molar mass of the gas.

Calculate the molar mass of hydrogen (\( H_2 \)) and helium (\( He \)). Remember that the molar mass should be in kilograms per mole (kg/mol) for use in the formula.

Plug in the values of \( T \) and \( m \) for both \( H_2 \) and \( He \) into the average speed formula to find the average speeds for both gases.

Compare the calculated average speeds of \( H_2 \) and \( He \) to determine which gas has a higher average speed at the given temperatures.

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Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. According to this theory, the average kinetic energy of gas particles is directly proportional to the temperature of the gas in Kelvin. This means that at higher temperatures, gas particles move faster, leading to higher average speeds.

Temperature Conversion

To compare the average speeds of H2 and He, it is essential to convert temperatures to the same scale. The temperature of H2 is given in Kelvin (150 K), while He's temperature is in Celsius (375 °C). The conversion from Celsius to Kelvin is done by adding 273.15, resulting in 648.15 K for He, which is crucial for accurate comparisons.

Molar Mass and Speed

The average speed of gas particles is inversely related to their molar mass, as described by Graham's law of effusion. Lighter gases, such as H2 (molar mass ≈ 2 g/mol), will generally have higher average speeds compared to heavier gases like He (molar mass ≈ 4 g/mol) at the same temperature. This relationship is important for determining which gas has a higher average speed under the given conditions.