Question

A 36 L tank of ammonia has a pressure of 11.5 kPa. Calculate the volume of the ammonia if its pressure is changed to 9.3 kPa while its temperature remains constant.

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` = 36L
• 
  `\sf P_1` =11.5KPa
• 
  `\sf P_2` = 9.3KPa

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 11.5 * 36= 9.3* V_2\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_2 = (11.5 * 36 )/(9.3)\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_2 = \cancel{( 414)/(9.3)}\\`

`\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf V_2 =44.5161.....\\`

`\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{V_2 = 44.52 \:L }\\`

Therefore, the volume of the ammonia will become 44.52 L if its pressure is changed to 9.3 kPa while its temperature remains constant.