Question

A gas is contained in a thick-walled balloon. When the pressure changes from 45.0 bar to 96.0 bar, the volume changes from 1.20 L to ____ L and the temperature changes from 314 K to 420 K.
What decimal or number goes in the blank?

Answer 1

Answer:

The final volume of the gas is 0.752 L.

Explanation:

Initial pressure of the gas =$P_1=45.0 bar$

Initial volume of the gas =$V_1=1.20L$

Initial temperature of the gas =$T_1=314 K$

Final pressure of the gas =$P_2=96.0 bar$

Final volume of the gas =$V_2=?$

Final temperature of the gas =$T_2=420 K$

Number of moles of gases are constant

Using an ideal gas equation :

$PV=nRT$

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

$V_2=\frac{45.0 bar\times 1.20 L\times 420 K}{314 K\times 96 bar}=0.752 L$

The final volume of the gas is 0.752 L.

Answer 2

P1 * V1 ÷ T1 = P2 * V2 ÷ T2  

45 * 1.20 ÷ 314 = 96 * V2 ÷ 420  

30,144 * V2 = 22,680  

V2 = 22,680 ÷ 30,144  

The new volume is approximately 0.75 liter.

I hope I helped