The mole fraction of CO2 in a certain solution with H2O as the solvent is 3.6 × 10−4. The
molality of CO2 in this solution is about:
A. 0.00036 m
B. 0.0065 m
C. 0.020 m
D. 2.0 × 10−5 m
E. 6.5 m
To find the molality of CO2 in the solution, we need to first understand the relationship between mole fraction and molality.
Mole fraction is defined as the ratio of the number of moles of the solute (CO2) to the total number of moles in the solution (CO2 + H2O). It can be calculated as follows:
Mole fraction (CO2) = moles of CO2 / (moles of CO2 + moles of H2O)
On the other hand, molality is defined as the number of moles of solute (CO2) per kilogram of solvent (H2O). It can be calculated using the formula:
Molality (CO2) = moles of CO2 / mass of H2O (in kg)
To obtain the molality, we need to convert the mole fraction of CO2 into moles of CO2. Since we don't have the total number of moles in the solution, we can assume an arbitrary mass for the solvent, such as 1 kg.
Let's calculate the number of moles of CO2 using the mole fraction:
Mole fraction (CO2) = moles of CO2 / (moles of CO2 + moles of H2O)
3.6 × 10^-4 = moles of CO2 / (moles of CO2 + 1)
Multiplying both sides by (moles of CO2 + 1):
3.6 × 10^-4 * (moles of CO2 + 1) = moles of CO2
Simplifying:
3.6 × 10^-4 * moles of CO2 + 3.6 × 10^-4 = moles of CO2
Rearranging the equation:
3.6 × 10^-4 = moles of CO2 - 3.6 × 10^-4 * moles of CO2
Combining like terms:
3.6 × 10^-4 = moles of CO2 * (1 - 3.6 × 10^-4)
Solving for moles of CO2:
moles of CO2 = (3.6 × 10^-4) / (1 - 3.6 × 10^-4)
Now we can calculate the molality using the obtained moles of CO2 and the assumed mass of H2O (1 kg):
Molality (CO2) = moles of CO2 / mass of H2O
Molality (CO2) = (3.6 × 10^-4) / 1
Molality (CO2) = 3.6 × 10^-4
Therefore, the molality of CO2 in this solution is approximately 0.00036 m, which corresponds to answer choice A.
To find the molality of CO2 in the solution, we first need to understand the relationship between mole fraction and molality.
Mole fraction is defined as the ratio of the number of moles of a particular component to the total number of moles in a solution. It is calculated by dividing the number of moles of the component by the total number of moles of all components in the solution.
Molality, on the other hand, is defined as the ratio of the number of moles of solute to the mass of the solvent in kilograms. It is calculated by dividing the number of moles of solute by the mass of the solvent in kilograms.
To convert from mole fraction to molality, we need to know the density of the solution. Since the density is not given in the question, we cannot directly calculate the molality. Therefore, it is not possible to determine the exact molality of CO2 in the solution with the information provided.
Therefore, none of the options provided (A, B, C, D, E) can be identified as the correct answer.
The definition of molal is
moles/kg solvent.
XCO2 = 3.6 x 10^-4
We take 1 mole of solution. That will contain 3.6 x 10^-4 moles CO2 and 1 kg solvent. How many grams CO2 is that?
3.6 x 10^-4 moles x (44 g/mol) = 0.0158 grams. How much will the solution weigh? If we had 1000 g solvent, that + 0.0158 g solute = 1000.0158 grams total
So we have 3 6 x 10^-4 moles/1.0000158 = ?? m