If 'M' is the molecular weight of a gas, what volume in L at STP would be occupied by M/4 of that gas

Options

A. 11.2
B. 22.4
C. 5.6
D. 22.4

Explanation

To solve the problem, we need to determine the volume of a gas at Standard Temperature and Pressure (STP) when we have a mass of \( \frac{M}{4} \), where \( M \) is the molecular weight of the gas.

### Step-by-Step Solution:

1. **Understand the Molecular Weight**:
- The molecular weight \( M \) of a gas is expressed in grams per mole (g/mol). This means that \( M \) grams of the gas corresponds to 1 mole of the gas.

2. **Determine the Amount of Gas**:
- We are given \( \frac{M}{4} \) grams of the gas. To find out how many moles this corresponds to, we can use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}} \]
- Substituting the values, we get:
\[ \text{Number of moles} = \frac{\frac{M}{4}}{M} = \frac{1}{4} \text{ moles} \]

3. **Volume of Gas at STP**:
- At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters. Therefore, the volume occupied by \( \frac{1}{4} \) moles of gas can be calculated as:
\[ \text{Volume} = \text{Number of moles} \times \text{Volume per mole} \]
- Substituting the values, we have:
\[ \text{Volume} = \frac{1}{4} \text{ moles} \times 22.4 \text{ L/mole} = \frac{22.4}{4} \text{ L} = 5.6 \text{ L} \]

4. **Final Answer**:
- The volume occupied by \( \frac{M}{4} \) grams of the gas at STP is **5.6 liters**.