Carbon dioxide gas has a Henry's law constant of 4.48×10-5 M/mmHg at 25.0 °C when dissolving in water. If the total pressure of gas (CO2 gas plus water vapor) over water is 1.00 atm, what is the concentration of CO2 in the water in grams per milliliter?
Pressure of the water vapor at 25.0 °C = 23.8 mmHg
To find the concentration of CO2 in the water in grams per milliliter, we can use Henry's law equation:
C = kH * P
where C is the concentration of CO2 in the water, kH is the Henry's law constant, and P is the partial pressure of the CO2 gas.
First, let's calculate the partial pressure of the CO2 gas:
Partial pressure of CO2 gas = Total pressure - Pressure of water vapor
Partial pressure of CO2 gas = 1.00 atm - 23.8 mmHg
Since we have different units for total pressure and pressure of water vapor, we need to convert the pressure of water vapor to atm:
Pressure of water vapor in atm = 23.8 mmHg / 760 mmHg/atm
Now, let's substitute the values into the equation:
Partial pressure of CO2 gas = 1.00 atm - (23.8 mmHg / 760 mmHg/atm)
Next, we can calculate the concentration of CO2 in the water:
C = (4.48 × 10^-5 M/mmHg) * (Partial pressure of CO2 gas)
Lastly, we need to convert the concentration from M/mmHg to g/mL:
Concentration in g/mL = (C * molar mass of CO2) / (density of water)
The molar mass of CO2 is approximately 44.01 g/mol, and the density of water is approximately 1 g/mL.
Now, let's calculate the concentration of CO2 in the water in grams per milliliter step-by-step.
To find the concentration of CO2 in the water in grams per milliliter, we need to use Henry's law equation:
C = k * P
Where:
C is the concentration of CO2 in the water (in molarity)
k is Henry's law constant
P is the partial pressure of CO2 (in mmHg)
First, we need to calculate the partial pressure of CO2. We know that the total pressure of the gas above the water is 1.00 atm, and the pressure of the water vapor is 23.8 mmHg. Therefore, the partial pressure of CO2 is:
Partial pressure of CO2 = Total pressure - Pressure of water vapor
Partial pressure of CO2 = 1.00 atm - 23.8 mmHg
Next, we need to convert the units to have consistent values. We can convert the total pressure to mmHg by multiplying it by 760:
Total pressure = 1.00 atm * 760 mmHg
Now we can calculate the partial pressure of CO2:
Partial pressure of CO2 = 760 mmHg - 23.8 mmHg
Once we have the partial pressure of CO2, we can use Henry's law constant to calculate the concentration of CO2 in molarity:
C = (Henry's law constant) * (Partial pressure of CO2)
C = 4.48×10-5 M/mmHg * (Partial pressure of CO2)
Finally, to convert the concentration from molarity to grams per milliliter, we need to use the molar mass of CO2 (44.01 g/mol):
Concentration in grams per milliliter = (Concentration in molarity) * (Molar mass of CO2)
Concentration in grams per milliliter = (C) * (44.01 g/mol)
C = KpP
C = 4.48E-5*(760mm-23.8mm) = ? mols/L.
Then ? x 44 = grams/L. Convert to g/mL.