Answer to Question #66230 in General Chemistry for Chris

Question

Changes in Volume:
Part A
A certain amount of chlorine gas was placed inside a cylinder with a movable piston at one end. The initial volume was 3.00 L and the initial pressure of chlorine was 1.35 atm . The piston was pushed down to change the volume to 1.00 L. Calculate the final pressure of the gas if the temperature and number of moles of chlorine remain constant.


Part B
In an air-conditioned room at 19.0 ∘C, a spherical balloon had the diameter of 50.0 cm. When taken outside on a hot summer day, the balloon expanded to 51.0 cm in diameter. What was the temperature outside in degrees Celsius? Assume that the balloon is a perfect sphere and that the pressure and number of moles of air molecules remains the same.

Answer 1

Changes in Volume:
Part A
A certain amount of chlorine gas was placed inside a cylinder with a movable piston at one end. The initial volume was 3.00 L and the initial pressure of chlorine was 1.35 atm . The piston was pushed down to change the volume to 1.00 L. Calculate the final pressure of the gas if the temperature and number of moles of chlorine remain constant.
Solution:
We use Boyle's law
P1 / P2 = V2 / V1
P2 = V1 P1 / V2
P2 = 3.00 L x 1.35 atm / 1.00 L = 4.05 atm
Answer: 4.05 atm
Part B
In an air-conditioned room at 19.0 ∘C, a spherical balloon had the diameter of 50.0 cm. When taken outside on a hot summer day, the balloon expanded to 51.0 cm in diameter. What was the temperature outside in degrees Celsius? Assume that the balloon is a perfect sphere and that the pressure and number of moles of air molecules remains the same.
Solution:
We use Charles's law
V1 / V2 = T1 / T2
The volume changed by the ratio
V1 / V2 = 51³ / 50³ = 1.0612
T1 = 19.0 ∘C + 273.15 = 292.15 K
T2 = 1.0612 x 292.15 K = 310 K
T2 = 310 K - 273.15 K = 36.85 ∘C

Answer: 36.85 ∘C