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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?

Respuesta :

quasarJose

Answer:

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

kudzordzifrancis

Answer:

50.5ml

Explanation:

From Boyle's gas law equation ,[tex]P_1V_1 = P_2V_2[/tex]

Where, [tex]P_1[/tex] and [tex]V_1[/tex] are the initial volume and initial pressure respectively, and, [tex]V_2[/tex] and [tex]P_2[/tex] are also the final volume and final pressure respectively.

But 1 atm=101.325kPa

We can deduce the following from the question.

[tex]V_1=25ml[/tex]

[tex]P_1=100kPa=0.99kPa[/tex]

[tex]P_2 = 50kPa= 0.49kPa[/tex]

By substitution,

[tex]0.99kPa \times 25ml=0.49kPa \times V_2[/tex]

Dividing through by 0.49kPa.

[tex] \implies \frac{0.99kPa \times 25ml}{0.49kPa}=\frac{0.49kPa \times V_2}{0.49kPa} [/tex]

[tex]\implies V_2 =2.02\times 25ml[/tex]

[tex]\implies V_2 =50.5ml[/tex]