One liter of a gas weighs $2 g$ at $300 K$ and $1 a t m$ pressure. If the pressure is made $0.75 a t m$ , at which of the following temperatures will one liter of the same gas weight one gram?

450 K

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600 K

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800 K

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900 K

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Solution

The correct option is A $450 K$
Solution:
Assembling all the data we get:
$T_{1} = 300 K T_{2} = ?$
$V_{1} = 1 L V_{2} = 1 L$
$P_{1} = 1 a t m; P_{2} = 0.75 a t m$
mass $= 2 g;$ mass $= 1 g$
so by formula $P V = n R T$
$\Rightarrow P V = \frac{m}{M} R T$
$M_{1} = M_{2}$
$\Rightarrow \frac{m_{1} R T_{1}}{P_{1} V_{1}} = \frac{m_{2} R T_{2}}{P_{2} V_{2}}$
$= \frac{2 \times 300}{1 \times 1} = \frac{1 \times T_{2}}{0.75 \times 1}$
$\Rightarrow T_{2} = 0.75 \times 600$
$= 450 K$

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One liter of a gas weighs 2g at 300K and 1atm pressure. If the pressure is made 0.75atm, at which of the following temperatures will one liter of the same gas weight one gram?

The correct option is A 450KSolution:Assembling all the data we get:T1=300KT2=?V1=1LV2=1LP1=1 atm;P2=0.75 atmmass =2g; mass =1 gso by formula PV=nRT⇒ PV=mMRTM1=M2⇒ m1RT1P1V1=m2RT2P2V2=2×3001×1=1×T20.75×1⇒ T2=0.75×600=450 K

One liter of a gas weighs $2 g$ at $300 K$ and $1 a t m$ pressure. If the pressure is made $0.75 a t m$ , at which of the following temperatures will one liter of the same gas weight one gram?