A 23.0% by mass LiCl solution is prepared in water. What is the mole fraction of the water?
To find the mole fraction of water in a solution, we need to calculate the moles of water and moles of LiCl separately.
Given:
- Mass percent of LiCl = 23.0%
- Mass percent of water = 100% - 23.0% = 77.0%
Step 1: Calculate the moles of LiCl
Assuming we have 100 grams of the LiCl solution:
Mass of LiCl = 23.0 grams (23.0% of 100 grams)
Molar mass of LiCl = 6.94 g/mol (lithium) + 35.45 g/mol (chlorine) = 42.39 g/mol
Moles of LiCl = Mass of LiCl / Molar mass of LiCl
Moles of LiCl = 23.0 g / 42.39 g/mol
Moles of LiCl = 0.543 mol
Step 2: Calculate the moles of water
Mass of water = 100 grams - 23.0 grams (mass of LiCl)
Mass of water = 77.0 grams
Molar mass of water = 18.02 g/mol
Moles of water = Mass of water / Molar mass of water
Moles of water = 77.0 g / 18.02 g/mol
Moles of water = 4.27 mol
Step 3: Calculate the mole fraction of water
Mole fraction of water = Moles of water / (Moles of LiCl + Moles of water)
Mole fraction of water = 4.27 mol / (0.543 mol + 4.27 mol)
Mole fraction of water ≈ 0.887
To find the mole fraction of water in a 23.0% by mass LiCl solution, you need to consider the mass of water and the mass of LiCl in the solution. The mole fraction (X) of a component in a solution is defined as the ratio of moles of that component to the total moles of all components.
To calculate the mole fraction of water, you first need to determine the moles of LiCl and the moles of water in the solution.
Let's assume we have a solution of 100 grams. This means that 23 grams of it is LiCl and the rest, 77 grams, is water.
To find the moles of LiCl, you need to divide the mass of LiCl by its molar mass. The molar mass of LiCl can be found by adding the molar masses of lithium (Li) and chlorine (Cl). The atomic mass of lithium is approximately 6.94 g/mol, and the atomic mass of chlorine is approximately 35.45 g/mol. Therefore, the molar mass of LiCl is approximately 6.94 + 35.45 = 42.39 g/mol.
Next, calculate the moles of LiCl by dividing its mass by its molar mass:
moles of LiCl = mass of LiCl / molar mass of LiCl
moles of LiCl = 23 g / 42.39 g/mol
To find the moles of water, divide the mass of water by its molar mass. The molar mass of water (H2O) is approximately 18.015 g/mol.
moles of water = mass of water / molar mass of water
moles of water = 77 g / 18.015 g/mol
Now that we have the moles of LiCl and water, we can calculate the mole fraction of water. The mole fraction of water is calculated by dividing the moles of water by the sum of the moles of LiCl and water.
mole fraction of water = moles of water / (moles of LiCl + moles of water)
Using the values we calculated earlier:
mole fraction of water = (77 g / 18.015 g/mol) / [(23 g / 42.39 g/mol) + (77 g / 18.015 g/mol)]
By simplifying this expression, the mole fraction of water in the 23.0% LiCl solution can be determined.
23% w/w LiCl means
23 g LiCl in (23g LiCl + 77 g H2O).
mols LiCl = 23/molar mass LiCl
mols H2O = 77/molar mass H2O
XH2O = mols H2O/total mols.