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.

Step-by-step 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 * (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 * (0.00131579 atm)/(1 torr)\\= 2 atm`

Formula used to calculate final temperature is as follows.

`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))`

Substitute the values into above formula as follows.

`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))\\(1 atm * 5 L)/(346 K) = (2 atm * V_(2))/(400 K)\\V_(2) = 2.89 L`

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