Two vessels are labeled a and b. vessel a contains nh3 gas at 70°c, and vessel b contains he gas at the same temperature. if the average kinetic energy of nh3 is 7.1x10^(-21) j/molecule, calculate the mean-square speed of he atoms in m^2/s^2.

Explanation:

1) Since the average kinetic energy of a gas is only dependent on its temperature, you conclude that, at the same temperature of 70°C, the average kinetic energy of He atoms is the same that the average kinetic energy of NH₃ molecules: 7.1 × 10⁻²¹ J / molecule.

2) Now, you can use the equation that relates the average kinetic energy with the mean-square speed:

Where:

You need to use the atomic mass of helium to find the mass (average) of one atom of helum:

        m = 4.003 g/ mol / (6.022 × 10²³ atoms/mol)

        m = 6.647 × 10⁻²⁴ g = 6.647 10 ⁻²⁷ kg / atom

3) Solve for v², substitute, and compute:

Note: since He is a monoatomic molecule, kg/atom = kg/molecule.

            = 2.14 × 10⁶ m²/s² ← answer

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