Calculate the molality of acetone in an
aqueous solution with a mole fraction for ace-
tone of 0.171.
Answer in units of m
Assume you have 1 mol of soln; therefore,
Xacetone = 0171
XH2O = 0.829
g H2O = 0.829*molar mass H2O = approximately 14.9 mL H2O or 0.0149 kg.
Then m = mols acetone/kg H2O =0.171/0.0149 = ?m
To calculate the molality of a solute in a solution, you need to know the mole fraction of the solute. In this case, we are given that the mole fraction of acetone (CH3COCH3) is 0.171.
The formula for molality (m) is defined as the moles of solute divided by the mass of the solvent in kilograms. It can be calculated using the following formula:
molality (m) = moles of solute / mass of solvent (in kg)
To find the molality, we need to assume a specific amount of acetone and water in the solution. Let's assume we have 1 mol of acetone and water combined.
From the given information, we know that the mole fraction of acetone is 0.171. The mole fraction is defined as the ratio of moles of acetone to the total moles of the solution.
So, we can write the equation as follows:
0.171 = moles of acetone / (moles of acetone + moles of water)
Since we assumed 1 mol of total solution, the moles of water will be (1 - moles of acetone).
We can rearrange the equation to solve for the moles of acetone:
0.171 = moles of acetone / (moles of acetone + (1 - moles of acetone))
Simplifying the equation:
0.171 = moles of acetone / 1,
0.171 = moles of acetone.
So, we found that the moles of acetone is 0.171 mol.
Next, we need to know the mass of the solvent in kilograms. Assuming 1 mol of solution, the mass of the solvent will be the molar mass of water. The molar mass of water is approximately 18 g/mol.
Converting grams to kilograms:
mass of solvent = (1 mol of solution - 0.171 mol of acetone) * (18 g/mol) / (1000 g/kg) = 0.6672 kg
Finally, we can plug the values into the formula for molality:
molality (m) = moles of solute / mass of solvent (in kg)
molality (m) = 0.171 mol / 0.6672 kg ≈ 0.257 m
Therefore, the molality of acetone in the aqueous solution with a mole fraction of 0.171 is approximately 0.257 m.