Question

1. The gas inside a balloon exerts a pressure of 3atm at

298 K. What is the temperature required to increase
the pressure to 5 atm?
​

Answer 1

497 K

Step-by-step explanation:

Assuming that the volume of the balloon (and so, the gas) remains constant, we can solve the problem by using the pressure's Law:

"When a constant mass of an ideal gas is kept at constant volume, the pressure of the gas is directly proportional to its absolute temperature"

Mathematically:

`p\propto T`

where

p is the pressure of the gas

T is the absolute temperature

The equation can also be rewritten as

`(p_1)/(T_1)=(p_2)/(T_2)`

where:

`p_1 = 3 atm` is the initial pressure of the gas

`T_1=298 K` is the initial temperature of the gas

`p_2 = 5 atm` is the final pressure of the gas

Solving for T2, we find the final temperature:

`T_2=(p_2 T_1)/(p_1)=((5)(298))/(3)=497 K`