Mole Fraction of 1.222 M Solution in Water - Help Needed

[sophief]

Homework Statement

can anyone help me with this problem...i can't seem to figure it out:

A 1.222 M solution of a compound in water has a density of 1.3250g/mol at 20 degrees Celsius. what is the mole fraction of this solution? the compound has a molar mass of 97.80g/mol.

Homework Equations

The Attempt at a Solution

 

[Moonbear]

What attempts have you made so far?

 

[Blueshift5]

Sure, I would be happy to help you with this problem. To find the mole fraction of a solution, we need to know the moles of the solute and the total moles of the solution.

First, we need to find the moles of the solute. We can do this by using the molarity equation: M = moles of solute / liters of solution. Rearranging this equation, we get moles of solute = M x liters of solution. In this case, the molarity (M) is 1.222 and the liters of solution can be calculated by dividing the density (1.3250 g/mol) by the molar mass of water (18.02 g/mol). This gives us 0.0735 L of solution. Plugging these values into the equation, we get moles of solute = 1.222 x 0.0735 = 0.0898 moles.

Next, we need to find the total moles of the solution. This is simply the moles of solute (0.0898) plus the moles of water. Since we know the density of the solution (1.3250 g/mol) and the molar mass of water (18.02 g/mol), we can calculate the moles of water using the same equation as before: moles of water = density x liters of solution / molar mass of water. This gives us 1.3250 x 0.0735 / 18.02 = 0.0054 moles of water. Therefore, the total moles of the solution is 0.0898 + 0.0054 = 0.0952 moles.

Finally, to find the mole fraction, we divide the moles of solute by the total moles: mole fraction = moles of solute / total moles. This gives us a mole fraction of 0.0898 / 0.0952 = 0.943, or 94.3%. This means that 94.3% of the solution is made up of the solute, while the remaining 5.7% is water.

I hope this helps you solve the problem. Let me know if you have any further questions.