Question

A gas occupies 12 L of a container at 2.75 atm. What is the volume of the gas if the pressure becomes 7.25atm?

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` = 12 mL
• 
  `\sf P_1` = 2.75 atm
• 
  `\sf P_2` = 7.25 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 2.75 * 12= 7.25 * V_2\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_2 = (2.75 * 12 )/(7.25)\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_2 = \cancel{( 33)/(7.25)}\\`

`\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf V_2 = 4.5517........\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{V_2 = 4.56 \:mL }\\`

Therefore, the volume will become 4.56 mL if the pressure becomes 7.25atm.