In which of the following sysems at equlibrium and room temperature doubling the volume will shift the equlibrium to the right?

Options

A. `K_(2)+Cl_(2)hArr2HCl`
B. `2CO+O_(2)hArr2CO_(2)`
C. `N_(2)+3H_(2)hArr2NH_(3)`
D. `PCl_(5)hArrpCl_(3)+Cl_(2)`

Answer

To determine in which of the given systems at equilibrium doubling the volume will shift the equilibrium to the right, we need to analyze how changing the volume affects the concentrations of reactants and products in each system.

### Step-by-Step Solution:

1. **Understand the Effect of Volume Change on Equilibrium:**
- When the volume of a system at equilibrium is doubled, the concentration of all gaseous species decreases. This is because concentration is defined as the number of moles of a substance per unit volume. Therefore, increasing the volume decreases the concentration of both reactants and products.

2. **Le Chatelier's Principle:**
- According to Le Chatelier's principle, if a system at equilibrium is subjected to a change in conditions (like volume), the equilibrium will shift in the direction that counteracts that change. In this case, if the concentration of products decreases more than that of reactants, the equilibrium will shift to the right (towards the products).

3. **Identify the Reaction with Different Moles of Reactants and Products:**
- We need to analyze the reactions provided in the options. The key is to find a reaction where the number of moles of products is greater than the number of moles of reactants. This will ensure that a decrease in concentration of products will lead to a shift in equilibrium to the right.

4. **Evaluate Each Option:**
- Let's assume we have four options (A, B, C, D). We will evaluate each based on the stoichiometry of the reaction:
- **Option A:** Reactants → Products (e.g., 1 mole → 1 mole)
- **Option B:** Reactants → Products (e.g., 2 moles → 2 moles)
- **Option C:** Reactants → Products (e.g., 1 mole → 2 moles)
- **Option D:** PCl5 ⇌ PCl3 + Cl2 (1 mole → 2 moles)
- In Option D, we see that 1 mole of PCl5 decomposes into 2 moles (1 mole of PCl3 and 1 mole of Cl2). This means that there are more moles of products (2 moles) than reactants (1 mole).

5. **Conclusion:**
- Since in Option D, the number of moles of products is greater than that of reactants, when the volume is doubled and the concentration decreases, the equilibrium will shift to the right to produce more products.

### Final Answer:
The equilibrium will shift to the right in the system represented by the reaction: PCl5 ⇌ PCl3 + Cl2.