A mixture of O2 and SO2 is confined in a vessel at equilibrium. Which statement describes the conditions that are true for the mixture?
I. The mass of SO2 is greater
II. The average molecular velocity of the O2 is greater
III. The average kinetic energy of the O2 is greater than the average kinetic energy of the SO2
IV. The temperature of both gases is the same.
a. I only
b. II only
c. III only
d. II and III only
e. II and IV only
e. II and IV
Because the mass of O2 could be larger, and II and IV are right. So out of elimination, E is correct
The correct answer is b. II only.
Explanation:
In a mixture of gases at equilibrium, the average molecular velocity of each gas is directly proportional to the square root of its absolute temperature. Since both gases are at equilibrium in the same vessel, they have the same temperature. Therefore, the average molecular velocity of O2 is greater than that of SO2 because O2 has a lighter molecular weight than SO2. However, the mass of SO2 and the average kinetic energy of the gases are not mentioned, so statements I, III, and IV cannot be determined. Therefore, the only statement that can be concluded is statement II - the average molecular velocity of the O2 is greater.
To determine which statements are true for the mixture of O2 and SO2 at equilibrium, we need to understand some basic concepts.
1. At equilibrium, the forward and reverse reactions occur at equal rates, resulting in no net change in the concentrations of the reactants and products.
2. The average molecular velocity of a gas is directly proportional to the square root of its temperature. Therefore, comparing the average molecular velocities of different gases will give us insights into their relative temperatures.
3. According to the kinetic theory of gases, the average kinetic energy of a gas is directly proportional to its temperature.
Now, let's evaluate each statement and find the true ones:
I. The mass of SO2 is greater.
This statement is not related to the conditions of the equilibrium mixture. The mass of a gas does not affect its behavior at equilibrium. Therefore, statement I is not true.
II. The average molecular velocity of the O2 is greater.
Since the average molecular velocity of a gas is directly proportional to the square root of its temperature, if the average molecular velocity of O2 is greater, it means its temperature is greater. This statement can be true, so we keep it for consideration.
III. The average kinetic energy of the O2 is greater than the average kinetic energy of the SO2.
According to the kinetic theory of gases, the average kinetic energy of a gas is directly proportional to its temperature. Therefore, if the average kinetic energy of O2 is greater, it means its temperature is greater. This statement aligns with statement II, so we keep it for consideration.
IV. The temperature of both gases is the same.
This statement contradicts statements II and III, which indicate that the average molecular velocity and average kinetic energy of O2 are greater, suggesting a higher temperature. Therefore, statement IV is not true.
Based on the analysis, the true statements are II and III. Thus, the correct answer is (d) II and III only.