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Math  /  Algebra

QuestionWhat pressure of carbon dioxide is needed to maintain a CO2\mathrm{CO}_{2} concentration of 0.67 M in a can of grape soda if the constant for CO2\mathrm{CO}_{2} is 1.3×10−3M/1.3 \times 10^{-3} \mathrm{M} / atm at 25∘C25^{\circ} \mathrm{C} ?
Give your answer in atm to the nearest tenth. Do not put units in the answer space.

Studdy Solution

STEP 1

1. We are dealing with a solution of carbon dioxide in grape soda.
2. The concentration of carbon dioxide in the solution is 0.67 M.
3. The Henry's Law constant for carbon dioxide at 25∘C 25^{\circ} \mathrm{C} is 1.3×10−3M/atm 1.3 \times 10^{-3} \mathrm{M/atm} .
4. We need to find the pressure of carbon dioxide in atm.

STEP 2

1. Understand and apply Henry's Law.
2. Set up the equation using Henry's Law.
3. Solve for the pressure of carbon dioxide.

STEP 3

Understand and apply Henry's Law.
Henry's Law states that the concentration of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. The law can be expressed as:
C=k⋅P C = k \cdot P
where C C is the concentration of the gas, k k is the Henry's Law constant, and P P is the partial pressure of the gas.

STEP 4

Set up the equation using Henry's Law.
Given: - C=0.67 M C = 0.67 \, \mathrm{M} - k=1.3×10−3 M/atm k = 1.3 \times 10^{-3} \, \mathrm{M/atm}
Substitute these values into the Henry's Law equation:
0.67=1.3×10−3⋅P 0.67 = 1.3 \times 10^{-3} \cdot P

STEP 5

Solve for the pressure of carbon dioxide.
To find P P , divide both sides of the equation by 1.3×10−3 1.3 \times 10^{-3} :
P=0.671.3×10−3 P = \frac{0.67}{1.3 \times 10^{-3}}
Calculate the value:
P≈515.38 P \approx 515.38
Round to the nearest tenth:
The pressure of carbon dioxide is approximately 515.4 \boxed{515.4} atm.

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