Question

Which of the following is true for gas-phase reactions?

• A. Decrease in moles of the product increases the volume of the reaction mixture
• B. Increase in moles of the product does not affect the volume of the reaction mixture
• C. Increase in moles of the product increases the volume of the reaction mixture
• D. Increase in moles of the product decreases the volume of the reaction mixture

Hint:

In gas-phase reactions at constant pressure and temperature, the volume of the reaction mixture is proportional to the total number of moles (\( V \propto n \)).

Answer 1

The Correct Option is C

Step 1: Understand gas-phase reactions and volume. 
In gas-phase reactions, the volume of the reaction mixture is related to the number of moles of gas, assuming ideal gas behavior. The ideal gas law is: \[ PV = nRT, \] where \( P \) is pressure, \( V \) is volume, \( n \) is the total number of moles of gas, \( R \) is the gas constant, and \( T \) is temperature. 
Step 2: Analyze the effect of the number of moles. 
If the reaction occurs at constant pressure and temperature (common in open systems or reactors with pressure control): \[ V = \frac{nRT}{P}. \] Here, \( R \), \( T \), and \( P \) are constant, so volume \( V \) is directly proportional to the total number of moles \( n \): \[ V \propto n. \] In a gas-phase reaction, if the number of moles of products is greater than the number of moles of reactants, the total number of moles \( n \) increases as the reaction proceeds, increasing the volume of the reaction mixture.
Example: \( N_2 + 3H_2 \to 2NH_3 \). Reactants: 1 + 3 = 4 moles; products: 2 moles. The number of moles decreases, reducing the volume.
Example: \( 2H_2O \to 2H_2 + O_2 \). Reactants: 2 moles; products: 2 + 1 = 3 moles. The number of moles increases, increasing the volume.
The question asks about the effect of an “increase in moles of the product.” This refers to the reaction producing more moles of gaseous products than reactants, leading to an increase in the total number of moles in the mixture. 
Step 3: Evaluate the options. 
(1) Decrease in moles of the product increases the volume of the reaction mixture: Incorrect, as a decrease in moles (e.g., fewer moles of products than reactants) decreases the volume. Incorrect.
(2) Increase in moles of the product does not affect the volume of the reaction mixture: Incorrect, as an increase in moles directly increases the volume at constant \( P \) and \( T \). Incorrect.
(3) Increase in moles of the product increases the volume of the reaction mixture: Correct, as more moles of gaseous products increase the total number of moles, thus increasing the volume. Correct.
(4) Increase in moles of the product decreases the volume of the reaction mixture: Incorrect, as an increase in moles increases the volume, not decreases it. Incorrect.
Step 4: Select the correct answer. 
For gas-phase reactions at constant pressure and temperature, an increase in moles of the product increases the volume of the reaction mixture, matching option (3).