For the chemical reaction
`3X(g)+Y(g) hArr X_(3)Y(g)`,
the amount of `X_(3)Y` at equilibrium is affected by

Options

A. Temperature and pressure
B. Temperature only
C. Pressure only
D. Temperature, pressure, and catalyst

Explanation

To determine the factors that affect the amount of \( X_3Y \) at equilibrium for the reaction:

\[ 3X(g) + Y(g) \rightleftharpoons X_3Y(g) \]

we can follow these steps:

### Step 1: Calculate the change in the number of moles of gas (\( \Delta n_g \))

The change in the number of gaseous molecules can be calculated using the formula:

\[ \Delta n_g = n_{\text{products}} - n_{\text{reactants}} \]

For the given reaction:
- **Products**: \( X_3Y \) has 1 mole.
- **Reactants**: \( 3X + Y \) has \( 3 + 1 = 4 \) moles.

Thus,

\[ \Delta n_g = 1 - 4 = -3 \]

### Step 2: Analyze the effect of pressure and volume on equilibrium

Since \( \Delta n_g \) is not equal to 0, changes in pressure and volume will affect the equilibrium position. According to Le Chatelier's principle, if we increase the pressure (or decrease the volume), the equilibrium will shift towards the side with fewer moles of gas. In this case, that is the product side, which means more \( X_3Y \) will be formed.

### Step 3: Consider the effect of temperature on equilibrium

The equilibrium constant \( K_c \) for the reaction is dependent on temperature. As temperature increases, \( K_c \) may increase or decrease depending on whether the reaction is exothermic or endothermic. If the reaction is endothermic, increasing temperature will shift the equilibrium to the right, producing more \( X_3Y \). If it is exothermic, increasing temperature will shift it to the left, producing less \( X_3Y \).

### Step 4: Evaluate the effect of catalysts

A catalyst speeds up the rate of reaching equilibrium but does not affect the position of equilibrium or the amount of products formed at equilibrium. Therefore, it does not affect the amount of \( X_3Y \).

### Conclusion

The amount of \( X_3Y \) at equilibrium is affected by:
1. **Temperature** - because it affects \( K_c \).
2. **Pressure** - because it shifts the equilibrium position.
3. **Catalyst** - does not affect the equilibrium amount.

Thus, the correct answer is that the amount of \( X_3Y \) at equilibrium is affected by temperature and pressure.