One litre 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 what temperatures will one litre of the same gas, weigh one gram?

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Solution

Step 1. Given data
$1 L$ of a gas weighs $2 g$ at $300 K$ and $1 a t m$ pressure
The pressure is made $0.75 a t m$ with $1 L$ of same gas
Initially the weight of the gas is $2 g$ but the final weight is $1 g$
Step 2. Formula used
Ideal gas equation $= P V = n R T$
$n = \frac{W}{M_{w}}$
Where $P$ is the pressure, $V$ is the volume $T$ is the temperature, $R$ is the universal gas constant , $n$ is the number of moles of gas, $W$ the weight of the gas and $M_{w}$ is the molecular weight of the gas
Step 3. Find the temperature
From ideal gas equation we get $P V = n R T$
$P_{1} = 1 P_{2} = 0.75 V_{1} = 1 V_{2} = 1 T_{1} = 300 W_{1} = 2 W_{2} = 1 \Rightarrow \frac{P_{1} V_{1}}{P_{2} V_{2}} = \frac{n_{1} T_{1}}{n_{2} T_{2}} \Rightarrow \frac{1 \times 1}{0.75 \times 1} = \frac{\frac{2}{M_{w}} \times 300}{\frac{1}{M_{w}} \times T_{2}} [∵ n = \frac{W}{M_{w}}] \Rightarrow T_{2} = 450 K$
Hence the temperature is $450 K$

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One litre of a gas weighs 2gat 300Kand 1atm pressure. If the pressure is made 0.75atm at what temperatures will one litre of the same gas, weigh one gram?

One litre 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 what temperatures will one litre of the same gas, weigh one gram?