Chemistry Hw Gas Laws

Question

Q1. A container of gas is initially at 25L, 0.500 atm and 25 ˚C. What will the pressure be at 69 ˚C if volume decreased to 13L?

Answer 1

layout of solving problem

(1) identify given variables

(2) use PV = nRT to differentiate between variables and constants [cross out constants + keep variables]

(3) generate new ideal gas equation fit for this specific problem

(4) plug in given information and find missing variable/variable asked for in problem

V₁ = 25L

V₂ = 13L

T₁= 25ºC

T₂ = 69ºC

P₁ = 0.500 atm

P₂ = ?

Since the only variables used here are pressure, volume, and temperature, we can infer that moles of (n) stays constant, and R(constant) cancels out. Also, note that usually temperature should be converted to K (Kelvins) because that's the appropriate unit for ideal gas laws; however, in this case, the temperature doesn't need to be converted into Kelvin.

The derived equation, based on the given information:

PV= nRT ⇒ P₁V₁/T₁ = P₂V₂/T₂

Solve for P₂ by rearranging and plugging given information in:

P₁V₁T₂/T₁V₂ = P₂

P₂ = 2.7 atm

Theoretically, the given answer makes sense because as volume decreases, pressure increases.