`PCl_(5)(g)hArr PCl_(3)(g)+Cl_(2)(g)`, In above reaction, at equilibrium condition mole fraction of `PCl_(5)` is 0.4 and mole fraction of `Cl_(2)` is 0.3. Then find out mole fraction of `PCl_(3)`

Options

A. 0.3
B. 0.7
C. 0.4
D. 0.6

Answer

To find the mole fraction of \( PCl_3 \) in the equilibrium reaction given by:

\[ PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g) \]

we know the following:

1. The mole fraction of \( PCl_5 \) is \( 0.4 \).
2. The mole fraction of \( Cl_2 \) is \( 0.3 \).

### Step-by-Step Solution:

**Step 1: Understand the concept of mole fractions.**
Mole fraction is defined as the ratio of the number of moles of a particular component to the total number of moles in the mixture.

**Step 2: Write the equation for the total mole fractions.**
The sum of the mole fractions of all components in the reaction must equal 1:

\[ \text{Mole fraction of } PCl_5 + \text{Mole fraction of } PCl_3 + \text{Mole fraction of } Cl_2 = 1 \]

**Step 3: Substitute the known values into the equation.**
We know:
- Mole fraction of \( PCl_5 = 0.4 \)
- Mole fraction of \( Cl_2 = 0.3 \)

Substituting these values into the equation gives:

\[ 0.4 + \text{Mole fraction of } PCl_3 + 0.3 = 1 \]

**Step 4: Simplify the equation.**
Combine the known mole fractions:

\[ 0.4 + 0.3 + \text{Mole fraction of } PCl_3 = 1 \]

This simplifies to:

\[ 0.7 + \text{Mole fraction of } PCl_3 = 1 \]

**Step 5: Solve for the mole fraction of \( PCl_3 \).**
To find the mole fraction of \( PCl_3 \), subtract \( 0.7 \) from \( 1 \):

\[ \text{Mole fraction of } PCl_3 = 1 - 0.7 = 0.3 \]

### Final Answer:
The mole fraction of \( PCl_3 \) is \( 0.3 \).

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