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

the standard Ideal Gas Equation:

$$pV = nRT$$

Where:

• $$p$$ = Pressure
• $$V$$ = Volume
• $$n$$ = Number of moles
• $$R$$ = Gas constant
• $$T$$ = Temperature

We know that the number of moles ($$n$$) is equal to the mass of the gas ($$m$$) divided by its molar mass ($$M$$):

$$n = \frac{m}{M}$$

Substituting this back into the ideal gas equation:

$$pV = \left(\frac{m}{M}\right)RT$$

Rearranging the formula to isolate pressure ($$p$$):

$$p = \left(\frac{m}{V}\right) \frac{RT}{M}$$

Since density ($$d$$) is defined as mass per unit volume ($$d = \frac{m}{V}$$), we can substitute $$d$$ into the equation:

$$p = d \cdot \frac{RT}{M}$$
$$\text{Slope } (m) = \frac{RT}{M}$$

The slope of the line is directly proportional to the temperature ($$\text{Slope} \propto T$$).

• Higher Temperature $$\rightarrow$$ Steeper Slope (closer to the $$y$$-axis).
• Lower Temperature $$\rightarrow$$ Gentler Slope (closer to the $$x$$-axis).
  
  

Hence, Option B is correct.