Question

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?

Answer 1

50.5ml

Step-by-step explanation:

From Boyle's gas law equation ,
`P_1V_1 = P_2V_2`

Where,
`P_1` and
`V_1` are the initial volume and initial pressure respectively, and,
`V_2` and
`P_2` are also the final volume and final pressure respectively.

But 1 atm=101.325kPa

We can deduce the following from the question.

`V_1=25ml`

`P_1=100kPa=0.99kPa`

`P_2 = 50kPa= 0.49kPa`

By substitution,

`0.99kPa * 25ml=0.49kPa * V_2`

Dividing through by 0.49kPa.

`\implies (0.99kPa * 25ml)/(0.49kPa)=(0.49kPa * V_2)/(0.49kPa)`

`\implies V_2 =2.02* 25ml`

`\implies V_2 =50.5ml`

Answer 2

50.5mL

Step-by-step 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