Question

An unknown gas occupies 14.3L at a pressure of 30atm. What is the volume when the pressure is increased to 54atm?

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` = 14.3L
• 
  `\sf P_1` =30atm
• 
  `\sf P_2` = 54 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 30 * 14.3= 54* V_2\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_2 = (30 * 14.3 )/(54)\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_2 = \cancel{( 429)/(54)}\\`

`\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf V_2 =7.944..........\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{V_2 = 7.94 \:L }\\`

Therefore, the volume will become 7.94 L when the pressure is increased to 54 atm.