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.
p = k*c
Convert 2.90 g CO2/L to M, the calculate K from above.
Then substitute into c = p/k and solve for c in moles/L.
4.4 x 10^-4 g CO2/L
can someone show me a solution for this
To find the concentration of CO2 in the drink after it has been opened and come to equilibrium with the atmosphere, we can use the concept of Henry's Law. Henry's Law states that the concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid.
Let's start by writing down the given information:
- Concentration of CO2 when bottled: 2.90 g/L
- Pressure when bottled: 2.0 atm
- Partial pressure of CO2 in the atmosphere: 3.0 x 10^-4 atm
Now, we need to convert the concentration of CO2 given in grams per liter to moles per liter. The molar mass of CO2 is 44.01 g/mol.
Concentration of CO2 when bottled = 2.90 g/L
Molar mass of CO2 = 44.01 g/mol
Concentration of CO2 when bottled in moles/L = (2.90 g/L) / (44.01 g/mol)
Next, we can use Henry's Law to find the concentration of CO2 in the drink after equilibrium.
Henry's Law equation can be expressed as:
C = k * P
Where:
C is the concentration of the gas in the liquid
k is the Henry's Law constant for the specific gas-solvent pair
P is the partial pressure of the gas above the liquid
In this case, we are looking for the new concentration of CO2, so let's call it C'. The partial pressure of CO2, which we can assume remains constant when the drink is opened, is 2.0 atm, as stated when bottled.
C' * (3.0 x 10^-4 atm) = (2.90 g/L) / (44.01 g/mol)
Now we can solve for C' to find the concentration of CO2 in the drink after equilibrium.
C' = [(2.90 g/L) / (44.01 g/mol)] / (3.0 x 10^-4 atm)
Calculate the right-hand side of the equation to find C'.