The Henry's law constant for CO2 at 20°C is 3.7*10^-2 M/atm. What mass of CO2 (in grams) is present in 355 mL of soda drink if the pressure of CO2 in the can is 2.5 atmospheres at 20°C? (Assume the solubility of CO2 in the soda is the same as water)
To find the mass of CO2 in grams present in the soda drink, we need to use Henry's law and the ideal gas law.
Henry's law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Mathematically, we can express this relationship as:
C = k * P
Where:
C is the concentration of the gas in the liquid (in moles per liter, or Molarity)
k is the Henry's law constant
P is the partial pressure of the gas above the liquid (in atmospheres)
We can rearrange the equation to solve for C:
C = k * P
Now, let's calculate the concentration of CO2 in the soda drink:
C = (3.7 * 10^-2 M/atm) * (2.5 atm)
C = 9.25 * 10^-2 M
The concentration of CO2 in the soda drink is 9.25 * 10^-2 M.
Next, we need to convert the concentration to moles of CO2 using the volume of the soda drink:
355 mL = 0.355 L (since 1 mL = 0.001 L)
Now, let's determine the number of moles of CO2 in the soda drink:
moles of CO2 = concentration (M) * volume (L)
moles of CO2 = (9.25 * 10^-2 M) * (0.355 L)
moles of CO2 = 3.27875 * 10^-2 moles
Finally, we can calculate the mass of CO2 in grams using the molar mass of CO2:
molar mass of CO2 = 44.01 g/mol
mass of CO2 = moles of CO2 * molar mass of CO2
mass of CO2 = (3.27875 * 10^-2 moles) * (44.01 g/mol)
mass of CO2 = 1.443 g (rounded to three decimal places)
Therefore, approximately 1.443 grams of CO2 are present in 355 mL of the soda drink with a CO2 pressure of 2.5 atmospheres at 20°C.
C = p*k
C = 2.5*0.037
Solve for C in M.
M = mol/L. You know L and M, solve for mol.
mol = grams/molar mass. You know molar mass and mol, solve for grams.