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Step-by-Step Explanation
Step 1: Identify the Relevant Concept
The average kinetic energy (K.E.) of a single molecule of any ideal gas at a given temperature depends only on the absolute temperature. Specifically, for a molecule in an ideal gas, the average kinetic energy is given by:
$ \text{Average K.E. per molecule} = \frac{3}{2} k_B T \quad (\text{for a diatomic gas at moderate temperatures, the factor may differ slightly based on degrees of freedom, but crucially it remains proportional to }T).
In this scenario, both hydrogen and oxygen molecules in the flask are at the same temperature (27°C).
Step 2: Express the Dependence on Temperature
Regardless of their masses or the ratio of their masses present, the average kinetic energy per molecule depends only on the temperature (for ideal gases under common conditions). Since hydrogen and oxygen are both at the same temperature (27°C), their kinetic energies per molecule will be in the same ratio.
Step 3: Calculate the Ratio of Average Kinetic Energies
Because the temperature is the same for both gases, the average kinetic energy per molecule of hydrogen and oxygen is equal. Mathematically:
$ \frac{\text{K.E.}_{\text{hydrogen per molecule}}}{\text{K.E.}_{\text{oxygen per molecule}}} = \frac{\frac{3}{2} k_B T}{\frac{3}{2} k_B T} = 1.
Step 4: Conclude the Ratio
Hence, the ratio of average kinetic energies per molecule of hydrogen to oxygen is:
$ 1 : 1.
