Question

A gas occupies 100 mL at 150. kPa. Find its volume at 200. kPa. You must show all your work to receive credit. Be sure to identify which of the Gas Laws you will be using.
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Answer 1

The Boyle-Mariotte's law or Boyle's law is one of the laws of gases that relates the volume (V) and pressure (P) of a certain amount of gas maintained at constant temperature, as follows:

PV = k

where k is a constant.

We can relate the state of a gas at a specific pressure and volume to another state in which the same gas is at different P and V since the product of both variables is equal to a constant, according to the Boyle's law, which will be the same regardless of the state of the gas. In this way,

P₁V₁ = P₂V₂

Where P₁ and V₁ is the pressure and volume of the gas to a state 1 and P₂ and V₂ is the pressure and volume of the same gas in a state 2.

In this case, in the state 1 the gas occupies a volume V₁ = 100 mL at a pressure of P₁ = 150 kPa. Then, in the state 2 the gas occupies a volume V₂ (that we must calculate through the boyle's law) at a pressure of P₂ = 200 kPa.  Substituting these values in the previous equation and clearing V₂, we have,

P₁V₁ = P₂V₂ → V₂ = $\frac{P1V1}{P2}$  

→ V₂ = $\frac{100 mL x 150 kPa}{200 kPa}$

→ V₂ = 75 mL

Then, the volume occupied by the gas at 200 kPa is V₂ = 75 mL