Which of the following is a correct representation?

P_{1} d_{1} T_{1} = P_{2} d_{2} T_{2}

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\frac{d_{1} P_{1}}{T_{1}} = \frac{d_{2} P_{2}}{T_{2}}

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\frac{P_{1}}{d_{1} T_{1}} = \frac{P_{2}}{d_{2} T_{2}}

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\frac{P_{1} T_{1}}{d_{1}} = \frac{P_{2} T_{2}}{d_{2}}

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Solution

The correct option is C $\frac{P_{1}}{d_{1} T_{1}} = \frac{P_{2}}{d_{2} T_{2}}$
The ideal gas equation is $P V = n R T$ .

We know, no. of moles, $n$ = $\frac{m a s s}{M o l . m a s s}$ and density, $d$ = $\frac{m a s s}{v o l u m e}$

Using these two relations, the ideal gas equation can be modified as:

$P M = d R T$ ;
where, $M = M o l . m a s s$ and $d = d e n s i t y$ .

Now, for a given gas, M is constant and R is the universal gas constant.

Hence, $\frac{P}{d \times T}$ = constant.

or $\frac{P_{1}}{d_{1} T_{1}}$ = $\frac{P_{2}}{d_{2} T_{2}}$

Thus, option C is correct.

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