Boyle's Law states that the volume of a gas is inversely proportional to its pressure, assuming constant temperature. Mathematically:

P₁V₁ = P₂V₂

Where:

* P₁ = Initial pressure

* V₁ = Initial volume

* P₂ = Final pressure

* V₂ = Final volume

Given:

* V₁ = 2.4 L

* P₁ = 14.1 kPa

* P₂ = 84.6 kPa

To Find: V₂

Solution:

1. Plug the values into Boyle's Law equation:

(14.1 kPa) * (2.4 L) = (84.6 kPa) * V₂

2. Solve for V₂:

V₂ = (14.1 kPa * 2.4 L) / 84.6 kPa

V₂ ≈ 0.4 L

Therefore, the gas will occupy approximately 0.4 L at a pressure of 84.6 kPa.