If the concentration of CO2 is 2.90 g of CO2 per 1.00 L of soft drink when bottled under 2.0 atm of CO2 pressure, what will be the concentration of the CO2 in the drink after it has been opened and left to come to equilibrium with the atmosphere which has a CO2 partial pressure of 3.0 x 10-4 atm.
4.4X10-4 g CO2/l
To find the concentration of CO2 in the drink after it has been opened and left to come to equilibrium with the atmosphere, we can use the concept of partial pressure and Henry's Law.
1. Start by finding the amount of CO2 dissolved in the soft drink when it was bottled under 2.0 atm of CO2 pressure:
- Convert the given concentration from grams per liter (g/L) to moles per liter (mol/L).
- The molar mass of CO2 is approximately 44.01 g/mol.
- So, the concentration is (2.90 g CO2/ 44.01 g/mol) = 0.0659 mol/L.
- Use the ideal gas law to find the number of moles of CO2 dissolved in the soft drink:
- (2.0 atm) * (1.00 L) = (0.0821 L·atm/mol·K) * T * (0.0659 mol/L),
- Where T is the temperature in Kelvin. Assuming constant temperature, we can rearrange the equation to solve for T:
- T = (2.0 atm * 1.00 L) / (0.0821 L·atm/mol·K * 0.0659 mol/L) ≈ 38.8 K.
2. Now, we need to find the solubility constant (Henry's Law constant) to calculate the concentration of CO2 in the drink after it has come to equilibrium with the atmosphere:
- Henry's Law relates the concentration of a gas in a liquid to its partial pressure in the surrounding gas.
- The equation for Henry's Law is: C = k * P, where C is the concentration of the dissolved gas, k is the solubility constant, and P is the partial pressure of the gas.
- Rearrange the equation to solve for k: k = C / P.
- Substitute the known values: k = (0.0659 mol/L) / (2.0 atm).
3. Finally, use the solubility constant (k) and the CO2 partial pressure in the atmosphere (3.0 x 10^-4 atm) to calculate the concentration of CO2 in the drink after it has come to equilibrium:
- Concentration = k * P = (0.0659 mol/L) / (2.0 atm) * (3.0 x 10^-4 atm).
By plugging in the known values and performing the calculation, you will get the concentration of CO2 in the drink after it has come to equilibrium with the atmosphere.