Which of the following expression is true regarding gas laws?
( $w =$ weight, $m =$ molar mass)

\frac{T_{1}}{T_{2}} = \frac{M_{1} w_{2}}{M_{2} w_{1}}

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\frac{T_{1}}{T_{2}} = \frac{M_{2} w_{1}}{M_{1} w_{2}}

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\frac{T_{1}}{T_{2}} = \frac{M_{1} w_{1}}{M_{2} w_{2}}

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\frac{T_{2}}{T_{1}} = \frac{M_{1} w_{1}}{M_{2} w_{2}}

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Solution

The correct option is A $\frac{T_{1}}{T_{2}} = \frac{M_{1} w_{2}}{M_{2} w_{1}}$
According to ideal gas equation
$P V = n R T$
Where, $P =$ Pressure
$V =$ Volume
$n =$ No. of mole
$R =$ Gas constant
$T =$ Temperature
$n = \frac{w_{1}}{M_{1}}$
Where $w_{1} =$ weight of the gas
$m_{1} =$ Molar mass
Taking $P, V$ and $R$ constant for two gas 1 and 2

$T_{1} = \frac{P \times V \times M_{1}}{w_{1} \times R}$

$T_{2} = \frac{P \times V \times M_{2}}{w_{2} \times R}$

$\frac{T_{1}}{T_{2}} = \frac{M_{1} w_{2}}{M_{2} w_{1}}$

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