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 written as \( P = \frac{\rho R T}{M_0} \), let's break it down step by step.

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = absolute temperature

### Step 2: Relate Moles to Mass
The number of moles \( n \) can be expressed in terms of mass \( m \) and molar mass \( M_0 \):
\[ n = \frac{m}{M_0} \]
where:
- \( m \) = mass of the gas
- \( M_0 \) = molar mass of the gas

### Step 3: Substitute for Moles in the Ideal Gas Law
Substituting \( n \) in the ideal gas law gives:
\[ PV = \frac{m}{M_0}RT \]

### Step 4: Rearranging the Equation
Rearranging this equation to solve for pressure \( P \):
\[ P = \frac{mRT}{MV} \]

### Step 5: Express Mass Density
The mass density \( \rho \) is defined as:
\[ \rho = \frac{m}{V} \]
Substituting this into the pressure equation gives:
\[ P = \frac{\rho VRT}{M_0} \]

### Step 6: Final Form of the Equation
Rearranging the equation, we arrive at:
\[ P = \frac{\rho R T}{M_0} \]

### Conclusion
Thus, in the equation \( P = \frac{\rho R T}{M_0} \):
- \( \rho \) is the mass density of the gas,
- \( M_0 \) is the molar mass of the gas,
- \( T \) is the absolute temperature,
- \( R \) is the universal gas constant.