chem help please

Question

A sample of nitrogen gas at 0.804 atm is compressed to a new volume of 373 mL and now has a pressure of 806 mm Hg. What was the original volume in liters if the temperature remained 344.5^oC the entire time?

Answer 1

The Ideal Gas Law (PV = nRT) shows us that the pressure and volume of a gas are inversely related. For example, if the pressure increases, the volume decreases, assuming n (moles of gas) and T (temperature) remained constant (and R is always a constant). More generally, the pressure and volume of a gas multiply to generate a constant product.

We can use this idea to set up an equation for this particular problem:

P₁V₁ = P₂V₂ (initial pressure times initial volume equals resulting pressure times resulting volume)

(0.804 atm)(x L) = (806 mm Hg)(373 mL)

Unfortunately, our units aren't consistent, so let's convert:

1. (0.804 atm) * (760 mm Hg/1 atm) = 611.03991 mm Hg
2. 373 mL * (1 L / 1000 mL) = .373 L

Plugging into our equation, we get:

(611.03991 mm Hg)(x L) = (806 mm Hg)(.373 L)

x L = (806 mm Hg)(.373 L)/(611.03991 mm Hg) = 0.492 L or 492 mL.

This answer of 0.492 L or 492 mL checks out! We predicted that a compression results in a smaller volume than we must've started with — an initial volume of 492 mL is larger than the compressed 373 mL!