For the given ideal gas equation `PV=nRT`, answer the following questions:
An ideal gas will have maximum density when

Options

A. P=0.5 atm, T = 600K
B. P=2 atm, T = 150K
C. P=1 atm, T = 300K
D. P=1.0 atm, T = 500K

Answer

To determine when an ideal gas will have maximum density using the ideal gas equation \( PV = nRT \), we can follow these steps:

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

### Step 2: Relate Density to the Ideal Gas Equation
Density (\( D \)) is defined as mass per unit volume. For an ideal gas, we can express the number of moles \( n \) in terms of mass (\( m \)) and molar mass (\( M \)):
\[ n = \frac{m}{M} \]
Substituting this into the ideal gas equation gives:
\[ PV = \frac{m}{M}RT \]

### Step 3: Rearranging for Density
Rearranging the equation to express density, we have:
\[ D = \frac{m}{V} = \frac{PM}{RT} \]
This shows that density is directly proportional to pressure and molar mass, and inversely proportional to temperature.

### Step 4: Analyzing the Relationship
From the equation \( D = \frac{PM}{RT} \), we can see:
- Density (\( D \)) increases with increasing pressure (\( P \)).
- Density (\( D \)) decreases with increasing temperature (\( T \)).

### Step 5: Maximizing Density
To maximize density, we need to maximize the pressure and minimize the temperature:
- **Maximum Pressure**: Higher pressure will increase density.
- **Minimum Temperature**: Lower temperature will also increase density.

### Conclusion
An ideal gas will have maximum density when the pressure is at its highest possible value and the temperature is at its lowest possible value.