Can someone please solve this problem?

Question

An ideal gas is allowed to expand from 7.20 L to 46.8 L at constant temperature. By what factor does the volume increase?

factor: _________

The pressure will

1. decrease by that same factor.
2. increase by that same factor.

If the initial pressure was 109 atm, what is the final pressure?

𝑃final= _________ atm

Answer 1

An ideal gas is allowed to expand from 7.20 L to 46.8 L at constant temperature. By what factor does the volume increase?

In order to calculate the factor in which the volume increases, we must divide the two numbers.

46.8 L / 7.20 L = 6.5

Factor: 6.5

The pressure will

1. decrease by that same factor.
2. increase by that same factor.

The pressure decreases by that same factor (6.5) because pressure and volume are inversely proportional to each other. This means that as pressure increases, volume decreases and when pressure decreases, volume increase. Basically, they increase and decrease in opposite directions of each other. We know that the pressure and volume are inversely proportional to each other because of a derivation of the ideal gas law: Boyle's Law.

P₁V₁ = P₂V₂

Since, we can see that they are on the same side of the ideal gas law: PV = nRT, they are inversely proportional to each other. However, if they were on opposite sides (ex. V and n), they would be directly proportional to each other.

If the initial pressure was 109 atm, what is the final pressure?

Using Boyle's Law, we can calculate the final pressure:

P₁V₁ = P₂V₂

P₁ = first pressure

P₂ = second pressure

V₁ = first volume

V₂ = second volume

P₁ = 109 atm

P₂ = ?

V₁ = 7.20 L

V₂ = 46.8 L

Plugging those numbers in:

P₁V₁ = P₂V₂

(109 atm)(7.20 L) = P₂ (46.8 L) Solve using algebra

P₂ = 16.8 atm (3 significant figures)

P_{fina l} = 16.8 atm