Question

A 4L of gas is under a pressure of 6atm. what is the volume of the gas at 2atm?

Answer 1

Boyle's Law-

`\:\:\:\:\:\:\:\:\:\:\:\star\:\sf \underline{ P_1 \: V_1=P_2 \: V_2}\\`

(Pressure is inversely proportional to the volume)

Where-

• 
  `\sf V_1` = Initial volume
• 
  `\sf V_2` = Final volume
• 
  `\sf P_1` = Initial pressure
• 
  `\sf P_2` = Final pressure

As per question, we are given that -

• 
  `\sf V_1` = 4 L
• 
  `\sf P_1` =6 atm
• 
  `\sf P_2` = 2 atm

Now that we have all the required values and we are asked to find out the final volume, so we can put the values and solve for the final volume -

`\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\star\:\sf \underline{ P_1 \: V_1=P_2 \: V_2}`

`\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf 6 * 4= 2* V_2\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_2 = (6 * 4 )/(2)\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_2 = \cancel{( 24)/(2)}\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{V_2 = 12 \:L }\\`

Therefore, the new volume of the gas will become 12 L at 2atm.