100 mL of `PH_(3)` on decomposition produced phosphorus and hydrogen. The change in volume is

Options

A. 50 mL increase
B. 500 ml decrease
C. 900 mL decrease
D. nil

Explanation

To solve the problem, we need to analyze the decomposition of phosphine (PH₃) and how it affects the volume of gases produced.

### Step-by-Step Solution:

1. **Write the Balanced Chemical Equation**:
The decomposition of phosphine can be represented as:
\[ 2 \text{PH}_3 \rightarrow 3 \text{H}_2 + 2 \text{P} \]
Here, phosphine (PH₃) decomposes to produce hydrogen gas (H₂) and solid phosphorus (P).

2. **Determine the Initial Volume of PH₃**:
We are given that the initial volume of PH₃ is 100 mL.

3. **Calculate the Volume of Hydrogen Produced**:
According to the balanced equation, 2 volumes of PH₃ produce 3 volumes of H₂. Therefore, we can set up a proportion to find the volume of H₂ produced from 100 mL of PH₃:
\[ \text{Volume of H}_2 = \left(\frac{3 \text{ volumes of H}_2}{2 \text{ volumes of PH}_3}\right) \times 100 \text{ mL PH}_3 \]
\[ \text{Volume of H}_2 = \frac{3}{2} \times 100 \text{ mL} = 150 \text{ mL} \]

4. **Calculate the Change in Volume**:
The change in volume can be calculated by subtracting the initial volume of PH₃ from the final volume of H₂ produced:
\[ \text{Change in Volume} = \text{Volume of H}_2 - \text{Initial Volume of PH}_3 \]
\[ \text{Change in Volume} = 150 \text{ mL} - 100 \text{ mL} = 50 \text{ mL} \]

5. **Conclusion**:
Since phosphorus is a solid and does not contribute to the gas volume, the total change in gas volume is an increase of 50 mL.

### Final Answer:
The change in volume is **50 mL increase**.