Question

A steel bottle contains 20 L of gas at 10 atm and 27 °C. What is its volume at STP?​

Answer 1

Given:

A steel bottle contains 20 L of gas at 10 atm and 27 °C.

To find:

What is its volume at STP?​

Solution:

The volume of the gas in the steel bottle, V₁ = 20 L

The pressure inside the bottle, P₁ = 10 atm

The temperature inside the bottle, T₁ = 27 °C = 27 + 273 K = 300 K

At STP,

The pressure, P₂ = 1 atm

The temperature, T₂ = 273 K

Let "V₂ Litres" be the volume of the gas.

We know the Combined Gas Law as follows:

$\boxed{\bold{\frac{P_1V_1 }{T_1} = \frac{P_2V_2 }{T_2} }}$

Now, on substituting the given values in the Combined Gas Law, we get

$\frac{10\:\times\: 20 }{300} = \frac{1\:\times \:V_2 }{273}$

$\implies \frac{ 2 }{3} = \frac{ V_2 }{273}$

$\implies V_2 = \frac{273 \times 2}{3}$

$\implies V_2 = \bold{182\:L}$

Thus, its volume at STP is → 182 L.

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