An ideal gas equation can be written as `P = rho R T/ M_0` where `rho` and M are resp.

Options

A. mass density, mass of gas
B. number density, molar mass
C. mass density, molar mass
D. number density, mass of gas

Answer

To solve the question regarding the ideal gas equation expressed as \( P = \frac{\rho R T}{M_0} \), we need to identify what \( \rho \) and \( M_0 \) represent.

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Law**:
The ideal gas law is typically expressed as:
\[ PV = nRT \]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

2. **Relating Moles to Mass**:
The number of moles \( n \) can be expressed in terms of mass \( m \) and molar mass \( M \):
\[ n = \frac{m}{M} \]
Substituting this into the ideal gas law gives:
\[ PV = \frac{m}{M}RT \]

3. **Rearranging the Equation**:
Rearranging the equation to express pressure \( P \):
\[ P = \frac{mRT}{MV} \]

4. **Defining Density**:
The density \( \rho \) of the gas is defined as:
\[ \rho = \frac{m}{V} \]
Substituting this definition of density into the pressure equation gives:
\[ P = \frac{\rho RT}{M} \]

5. **Identifying \( \rho \) and \( M_0 \)**:
In the equation \( P = \frac{\rho R T}{M_0} \), we can compare it with the derived equation \( P = \frac{\rho RT}{M} \). From this comparison:
- \( \rho \) represents the **mass density** of the gas.
- \( M_0 \) corresponds to the **molar mass** (or molecular mass) of the gas.

### Final Answer:
- \( \rho \) is the **mass density** of the gas.
- \( M_0 \) is the **molar mass** (or molecular mass) of the gas.