A can of coke contains 25 mL of carbon dioxide gas at 100kPa. If you take it on a hike up Mount Everest and the pressure decreases to 50 kPa , what will the new volume of the carbon dioxide gas in your coke can be?

50.5mL

Explanation:

Given parameters:

Initial volume of coke V₁ = 25mL

            1 atm = 101.325kPa

Initial pressure on coke P₁ = 100kPa  = 0.99atm

Final pressure on top of mountain  = 50kPa  = 0.49atm

Unknown:

Final volume = ?

Solution:

To solve this problem, we simply apply Boyle's law.

Boyle's law states that "the volume of a fixed mass of gas is inversely proportional to pressure provided that temperature remains constant".

Mathematically;

             P₁V₁   = P₂V₂

where P and V are pressure and volume. 1 and 2 are initial and final states.

Input the parameters and solve for V₂;

              0.99 x 25  = V₂ x 0.49

                     V₂   = 50.5mL

50.5ml

Explanation:

From Boyle's gas law equation ,

Where, and are the initial volume and initial pressure respectively, and, and are also the final volume and final pressure respectively.

But 1 atm=101.325kPa

We can deduce the following from the question.

By substitution,

Dividing through by 0.49kPa.

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