Question

A balloon at -73C with 5L of gas is heated to 400K. If the pressure ranges from 101.3 kPa to 1520 torr; What will be the final volumn

Answer 1

Answer: The final volume will be 2.89 L.

Explanation:

Given: $T_{1} = 73^{o}C = (73 + 273) K = 346 K$,         $V_{1} = 5L$,          $T_{1} = 400 K$

$P_{1}$ = 101.3 kPa

Convert kPa to atm as follows.

$1 kPa = 0.00986923\\101.3 kPa = 101.3 kPa \times \frac{0.00986923 atm}{1 kPa}\\= 0.99 atm\\= 1 atm$

$P_{2}$ = 1520 torr

Convert torr into atm as follows.

$1 torr = 0.00131579 atm\\1520 torr = 1520 torr \times \frac{0.00131579 atm}{1 torr}\\= 2 atm$

Formula used to calculate final temperature 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.

$\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}\\\frac{1 atm \times 5 L}{346 K} = \frac{2 atm \times V_{2}}{400 K}\\V_{2} = 2.89 L$

Thus, we can conclude that the final volume will be 2.89 L.