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AIIMS 2002

Exam: AIIMS
Year: 2002
Subject: Chemistry
Chapter: States of Matter

AIIMS 2002 · Chemistry · States of Matter

If P is pressure and is density of a gas, then P and are related as

If

P

is pressure and

\rho

is density of a gas, then

P

and

\rho

are related as

Options

A $P \propto \rho$
B $P \propto(1 / \rho)$
C $P \propto \rho^2$
D $P \propto\left(1 / \rho^2\right)$ .

Correct answer

A. $P \propto \rho$

Step-by-step solution

Ideal gas equation is given as :

P V=n R TP=

Pressure of gas,

V=

volume of gas

n=

moles of gas,

R=

gas constant

T=

temperature

\begin{array}{rlrl} \Rightarrow \quadP V=\frac{w}{M}RT \quad & w & =\text{ mass\text{ of }\text{ gas } }\\ M & =\text{ Molecular mass of \text{ gas } } \end{array}

\begin{aligned}& P=\left(\frac{w}{V}\right)\frac{R T}{M} \RightarrowP=\rho \frac{R T}{M}\\ & \left(\operatorname{As} \rho=\frac{w}{V}\right)\\ \Rightarrow \quad & P \propto \rho \end{aligned}

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