A flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ} C$ The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:
- $2: 1$
- $1: 4$
- $1: 1$
- $4: 1$
The Correct Option is C
Solution and Explanation
The problem involves a flask containing hydrogen and oxygen in a 2:1 ratio by mass at a temperature of 27°C. We are asked to find the ratio of the average kinetic energy per molecule of hydrogen and oxygen, respectively.
Key Concept: The average kinetic energy (\( K.E. \)) of a molecule is given by the equation: \[ K.E. = \frac{3}{2} k_B T \] Where: - \( k_B \) is the Boltzmann constant, - \( T \) is the temperature in Kelvin.
The average kinetic energy is independent of the type of gas, meaning that the average kinetic energy per molecule of hydrogen is equal to the average kinetic energy per molecule of oxygen at the same temperature.
Step 1: Convert the given temperature into Kelvin: \[ T = 27^\circ C + 273 = 300 \, \text{K} \]
Step 2: Since both gases are at the same temperature (300 K), the average kinetic energy per molecule of hydrogen and oxygen will be the same, according to the kinetic theory of gases.
\[ K.E. (\text{Hydrogen}) = K.E. (\text{Oxygen}) \]
Step 3: The ratio of the average kinetic energy per molecule of hydrogen and oxygen is:
\[ \frac{K.E. (\text{Hydrogen})}{K.E. (\text{Oxygen})} = 1:1 \]
The correct answer is: (C) 1:1
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
