Question

A 2.0 mL sample of air in a syringe exerts a pressure of 1.02 atm at 22 C. If that syringe is placed into boiling water at 100 C and the pressure in the syringe increases to 1.27 atm, what is the new volume of the air in the syringe?

Answer 1

Answer: The new volume of the air in the syringe is 7.3 mL.

Explanation:

Given: $V_{1}$ = 2.0 mL,     $P_{1}$ = 1.02 atm,          $T_{1} = 22^{o}C$

$V_{2}$ = ?,               $P_{2}$ = 1.27 atm,               $T_{2} = 100^{o}C$

Formula used to calculate the new volume in syringe is as follows.

$\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}$

Substitute the values into above formula as follows.

$\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}\\\frac{1.02 atm \times 2.0 mL}{22^{o}C} = \frac{1.27 atm \times V_{1}}{100^{o}C}\\V_{1} = 7.3 mL$

Thus, we can conclude that the new volume of the air in the syringe is 7.3 mL.