Question

Which amongst the given plots is the correct plot for pressure \((p)\) vs density \((d)\) for an ideal gas?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B

To determine the correct plot for pressure \( (p) \) vs. density \( (d) \) for an ideal gas, we need to use the ideal gas law, which is represented by the equation:

PV = nRT

Here, \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature.

We can rearrange this equation to express pressure in terms of density:

P = \frac{nRT}{V}

Density \( d \) is defined as mass per unit volume \( (d = \frac{m}{V}) \). For n moles of a gas, mass can be expressed as \( m = nM \), where \( M \) is the molar mass. So, the density can be rewritten as:

d = \frac{nM}{V}

Substitute the expression for density into the ideal gas equation:

P = \frac{dRT}{M}

This equation shows that pressure \( P \) is directly proportional to density \( d \) when the temperature \( T \) and molar mass \( M \) are constants:

P \propto d

This indicates that the plot of pressure vs. density will be a straight line with a positive slope.

By analyzing the given options, we need to identify the plot that is a straight line passing through the origin, which represents a linear relationship. The correct plot for pressure vs. density for an ideal gas is:

This depicted graph represents the relationship correctly, as it shows a straight line, which is consistent with our derived equation showing direct proportionality between pressure and density.