The S.I. unit of volume of gas is measured in

Options

A. mL
B. `dm^3`
C. L
D. `m^2`

Answer

To determine the S.I. unit of volume of gas, we can analyze the ideal gas equation and its components step by step.

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Equation**:
The ideal gas equation is given by:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature

2. **Rearranging the Equation**:
To find the volume \( V \), we can rearrange the equation:
\[ V = \frac{nRT}{P} \]

3. **Identifying Units**:
We need to identify the units of each component in the equation:
- \( n \) (number of moles) is measured in moles (mol).
- \( R \) (universal gas constant) is typically given in joules per mole per kelvin (J/(mol·K)).
- \( T \) (temperature) is measured in kelvin (K).
- \( P \) (pressure) is measured in pascals (Pa), which is equivalent to newtons per square meter (N/m²).

4. **Substituting Units into the Volume Equation**:
Now, substituting the units into the volume equation:
\[ V = \frac{(mol) \cdot (J/(mol \cdot K)) \cdot (K)}{Pa} \]

5. **Simplifying the Units**:
When we simplify this, we notice:
- The moles (mol) in the numerator and denominator cancel out.
- The kelvin (K) in the numerator and denominator also cancel out.
Thus, we have:
\[ V = \frac{J}{Pa} \]

6. **Substituting Joules and Pascals**:
We know that:
- 1 joule (J) = 1 newton meter (N·m)
- 1 pascal (Pa) = 1 newton per square meter (N/m²)

Therefore, substituting these values gives:
\[ V = \frac{N \cdot m}{N/m²} = m³ \]

7. **Conclusion**:
Thus, the S.I. unit of volume of gas is:
\[ \text{Volume} = \text{meter cubed (m³)} \]

### Final Answer:
The S.I. unit of volume of gas is measured in **cubic meters (m³)**.