객관식
When molecules in a gas move more quickly, what is increased as a result?
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7. Gases
Kinetic Energy of Gases
객관식
In which of the following substances are the molecules moving the fastest, assuming all are at the same temperature?
A
Hydrogen gas (H_2)
B
Carbon dioxide (CO_2)
C
Nitrogen gas (N_2)
D
Oxygen gas (O_2)
검증된 단계별 안내1
Recall that the average kinetic energy of gas molecules depends only on temperature and is given by the equation \(\frac{1}{2} m v^2 = \frac{3}{2} k_B T\), where \(m\) is the mass of a molecule, \(v\) is the average speed, \(k_B\) is Boltzmann's constant, and \(T\) is the temperature in kelvin.
Since all gases are at the same temperature, their average kinetic energies are equal, so differences in molecular speed come from differences in molecular mass.
Use the relationship for root-mean-square speed of gas molecules: \(v_{rms} = \sqrt{\frac{3RT}{M}}\), where \(R\) is the gas constant, \(T\) is temperature, and \(M\) is the molar mass of the gas in kilograms per mole.
Compare the molar masses of the gases: Hydrogen gas (H\(_2\)) has the smallest molar mass (~2 g/mol), Nitrogen gas (N\(_2\)) is about 28 g/mol, Oxygen gas (O\(_2\)) is about 32 g/mol, and Carbon dioxide (CO\(_2\)) is about 44 g/mol.
Since \(v_{rms}\) is inversely proportional to the square root of molar mass, the gas with the smallest molar mass (Hydrogen gas) will have the fastest moving molecules at the same temperature.
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