Question

An atmospheric concentration of 380 ppm CO2 corresponds to a partial pressure of 0.00038 atm. What percentage of the CO2 originally dissolved in the solution in Part A remains in solution after the soft drink reaches equilibrium with the ambient atmosphere

Answer 1

Answer:

8.44 * 10^-3 %

Explanation:

The solubility of CO2 gas in water is 0.15g/100 ml at a CO2 pressure of 760 mmHg.

Determine the percentage of the CO2 that dissolved originally in the solution that remains

Amount remaining ( Sg = kpg )

Sg = solubility of gas = 0.15 / 100 g/ml

pg. = partial pressure of gas = 760 mmHg = 1 atm

therefore ; K = 1.5 * 10^-3 gm^-1 atm^-1

solubility of gas inside container

Sg = 0.675 * 10^-2 g/ml

solubility of gas during/after dissolution ( amount that remains )

sg = 1.5 * 10^-3 * 0.00038

    =  5.7 * 10^-7  g/ml

therefore the percentage remaining

= (5.7 * 10^-7  / 0.675 * 10^-2 ) * 100

= 8.44 * 10^-3 %

Answer 2

The percentage of CO2 remaining in the solution after the soft drink reaches equilibrium is 8.4 × 10⁻³ %

There exists some missing information in the question.

Let us assume that:

• the solubility of CO2 gas in the water = 0.15 g/100 mL = 1.5 × 10⁻³
• the partial pressure of CO2 = 760 mmHg = 1 atm

Then, by applying Henry's law:

$\mathbf{S_g = k P_g}$

$\mathbf{k = \dfrac{S_g}{P_g}}$

$\mathbf{k =\dfrac{1.5 \times 10^{-3} g/mL}{1\ atm}}}$

k = 1.5 × 10⁻³ g/m* atm

The percentage of CO2 that was originally dissolved in the solution is:

$\mathbf{S_g = k P_g}$

• Assuming the partial pressure of CO2 = 4.5 atm

Then;

$\mathbf{S_g = 1.5 \times 10^{-3} g/mL* atm \times 4.5 \ atm}$

$\mathbf{S_g =0.00675 \ g/mL}$

The partial pressure in the can when the soft drink is being opened is 0.00038 atm.

The solubility of the gas $\mathbf{S_g = 1.5 \times 10^{-3} g/mL* atm \times 0.00038 \ atm}$

$\mathbf{S_g =5.7 \times 10^7 \ g/mL}$

Thus, the percentage of CO2 remaining in the solution after the soft drink reaches equilibrium is:

$\mathbf{=\dfrac{5.7\times 10^{-7}}{0.00675} \times 100 \%}$

$\mathbf{=0.0084 \%}$

= 8.4 × 10⁻³ %

Learn more about Henry's Law here:

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