Question

A syringe of volume 16 cm3 is filled with air to a pressure of 1.03 atm. If the piston of the syringe is pushed to change the volume to 8.83 cm3 keeping the temperature constant, what is the new pressure of the air in the syringe in unit of kPa

Answer 1

Answer:

189.07 kPa

Explanation:

Concept tested: Boyle's law

We are given;

• Initial volume of the syringe, V1 is 16 cm³
• Initial pressure of the syringe, P1 is 1.03 atm
• New volume of the syringe, V2 is 8.83 cm³

We are required to calculate the new pressure of the syringe;

• We are going to use the concept on Boyle's law of gases.
• According to the Boyle's law, for a fixed mass of a gas, the pressure is inversely proportional to its volume at constant temperature.

• That is; P α 1/V

• At varying pressure and volume, k(constant)  = PV and P1V1=P2V2

Therefore, to get the new pressure, P2, we rearrange the formula;

P2 = P1V1 ÷ V2

     = ( 16 cm³ × 1.03 atm) ÷ 8.83 cm³

    = 1.866 atm.

• Thus, the new pressure is 1.866 atm
• But, we need to convert pressure to Kpa
• Conversion factor is 101.325 kPa/atm

Thus;

Pressure = 1.866 atm × 101.325 kPa/atm

               = 189.07 kPa

Hence, the new pressure of the air in the syringe is 189.07 kPa