Question

A sample of gas occupies 10 litres under a pressure of 1 atm,what will be its volume if the pressure is increased to 2 atm?Assume that the temperature of the gas does not changes.​

Answer 1

Given:

• Volume of gas when pressure = 1atm = 10L

To find:

• Volume of gas when pressure = 2atm = ?

Solution:

Using the formula

P1V1 = P2V2

Where

• P1 ; pressure of gas 1 = 10L
• V1 : volume of gas 2 = 1 atm
• P2 : pressure of gas 2 = 2 atm
• V2 : volume of gas 2 = ?

Substituting the values we have

→ 10 × 1 = 2 × V2

→ V2 = 10/2

→ V2 = 5 L

Hence , volume of gas 2 = 5L

★ Knowledge enhancer:

Derivation of formula ; P1V1 = P2V2

Using the gas law

Pressure directly proportional to 1/volume

Removing the proportionality

P = k/V

PV= k

If P1 = P2 & V1 = V2

P1V1 = P2V2

Hence , we got the formula

Answer 2

Answer:-

Given:

Initial Pressure $\sf (P_1)$ = 1 atm.

Initial Volume $\sf (V_1)$ = 10 L

Final Pressure $\sf (P_2)$ = 2 atm.

We know that,

Boyle's law of gases states that at constant temperature the pressure of a gas is inversely proportional to it's Volume.

$\sf \large\: P \: \: \alpha \: \: \frac{1}{V}$

→ PV = k (Constant)

$\implies\sf \: P _{1}V _{1} = P _{2}V_{2}$

$\implies\sf \: (1)(10) = (2)( V_{2})$

$\implies \sf \: V_{2} = \frac{10}{2}$

$\implies \sf \large \: V_{2} = 5 \: L$

Hence, the Volume of the gas decreases to 5 L.