Question

2.5 moles of a gas is enclosed in a 87.2 L cylinder with a moveable piston at 425 K and 1.0 atm. An additional 2.5 moles of gas is added to the system and it is cooled to 273 K. The cylinder changes volume to maintain the pressure. What is the volume in the final system?

Answer 1

Answer:

112 L

Explanation:

Since the pressure is being held constant, you can use the following variation of the Ideal Gas Law to find the new volume:

$\frac{V_1}{T_1N_1}=\frac{V_2}{T_2N_2}$

In this equation, "V₁", "T₁", and "N₁" represent the initial volume, temperature, and moles. "V₂", "T₂", and "N₂" represent the final volume, temperature, and moles.

V₁ = 87.2 L                             V₂ = ? L

T₁ = 425 K                              T₂ = 273 K

N₁ = 2.5 moles                       N₂ = 2.5 + 2.5 = 5.0 moles

$\frac{V_1}{T_1N_1}=\frac{V_2}{T_2N_2}$                                                   <----- Formula

$\frac{87.2 L}{(425K)(2.5 moles)}=\frac{V_2}{(273 K)(5.0 moles)}$                    <----- Insert values

$\frac{87.2 L}{1062.5}=\frac{V_2}{1365}$                                                    <----- Simplify denominators

$0.08207=\frac{V_2}{1365}$                                                 <----- Simplify left side

$112L={V_2}$                                                        <----- Multiply both sides by 1365