A solution of lithium chloride in water has a mole fraction of 0.0500 in LiCl. What is the molality?
Mole fraction = moles of LiCl over total moles of solution
Molality=moles of LiCl per kg of solvent
How do I link this information?
Assume you have 1.00 mol solution.
That means you have 0.05 mols LiCl and 0.95 mols H2O.
0.95 mol H2O x (18.015 g H2O/1 mol H2O) = 17.11 grams H2O.
So molality = mols/kg solvent=
0.05 mols LiCl/0.01711 kg solvent = xx molal.
To determine the molality of a solution, you need to link the mole fraction to the molality using the formula:
Molality = (moles of solute) / (mass of solvent in kg)
In this case, the solute is lithium chloride (LiCl) and the solvent is water. Given that the solution has a mole fraction of 0.0500, you can assume that there is a 0.0500 mole fraction of LiCl in the solution.
To calculate the molality, you first need to determine the moles of LiCl in the solution. Since the mole fraction is defined as the moles of LiCl over the total moles of the solution, you can express the moles of LiCl as:
moles of LiCl = mole fraction of LiCl * total moles of solution
Since the total moles of solution is not given, you cannot determine the exact value of moles of LiCl. However, you can assume that the total moles of solution is 1, so you can calculate the moles of LiCl as:
moles of LiCl = 0.0500 * 1
Next, you need to determine the mass of the solvent in kilograms. Since the solvent is water, you can assume that the density of water is 1 g/mL or 1000 kg/m³. Therefore, you can calculate the mass of the solvent as:
mass of solvent = volume of solvent * density of water
Since the volume of solvent is not given, you cannot directly calculate the mass of the solvent. However, you can assume that you have 1 kg of water as a solvent, so the mass of the solvent is 1 kg.
Finally, you can calculate the molality using the formula:
Molality = (moles of LiCl) / (mass of solvent in kg)
Substituting the values, you have:
Molality = (0.0500 * 1) / 1
Simplifying, the molality is equal to 0.0500 mol/kg.
To calculate the molality from the given information, you need to use the relationship between mole fraction and molality.
First, we can start by using the mole fraction formula:
Mole fraction of LiCl = moles of LiCl / total moles of solution
In this case, the mole fraction of LiCl is given as 0.0500. Now, let's assume that we have a certain amount of solution. We can represent the moles of LiCl in this solution as 'x'.
So, the mole fraction equation becomes:
0.0500 = x / (x + moles of water)
Now, to find the molality, we need to remember that molality is defined as moles of solute per kg of solvent. In this case, the solvent is water. So, we need to convert the mass of water to kg.
Here's how the calculation can be done step-by-step:
1. Determine the moles of LiCl:
From the mole fraction equation, we know that the moles of LiCl is equal to the mole fraction multiplied by the total moles of solution. Assuming we have 1 mol of solution, we can write:
x = 0.0500 * 1 = 0.0500 mol
2. Determine the moles of water:
In this case, the moles of water can be calculated by subtracting the moles of LiCl from the total moles of solution (which is also 1 mol in our case):
moles of water = 1 - 0.0500 = 0.9500 mol
3. Determine the mass of water:
The molar mass of water is approximately 18.015 g/mol. Therefore, the mass of water can be calculated by multiplying the moles of water by its molar mass:
mass of water = 0.9500 mol * 18.015 g/mol = 17.11425 g
4. Convert the mass of water to kg:
To convert the mass of water to kg, divide by 1000 (since there are 1000 grams in a kilogram):
mass of water in kg = 17.11425 g / 1000 = 0.01711425 kg
5. Calculate the molality:
Finally, we can calculate the molality by dividing the moles of LiCl by the mass of water in kg:
molality = moles of LiCl / mass of water in kg
= 0.0500 mol / 0.01711425 kg
Therefore, the molality is approximately:
molality ≈ 2.9192 mol/kg