A solution contains 40.0 g of sodium chloride and 200.0 g of water. Calculate the NaCl

concentration as a a) mass percentage, b) molality, c) mole fraction.

I have trouble finding mole fraction. I believe I've got the other two, but I'm not 100% sure.

% w/w = 16.7

m = 3.42
If you didn't get these show your work and I'll find the error.

mols NaCl = grams/molar mass
mols H2O = grams/molar mass
XNaCl = mols NaCl/total mols.
I worked it quickly and obtained 0.381 but you should confirm that.
As a check run XH2O and see if you get 1-0.381 because XNaCl + XH2O must = 1.00(within rounding error).

Dr.Bob, Could you please show the work for w/w and mol frac. I continue to get a completely bizarre number. The only one that I am getting correct is the molal part.

I was able to find both the Mol Frac and m now. The only problem is w/w.

m) (40.0gNaCl)*(1molNaCl/58.33gNaCl)=.684mol Nacl
-200.0gH20*(1molH20/18.02gH20)=11.mol H20
-200g= .2L
** .684mol NaCl/.2LH20= m=3.42

Mol Frac) .864molNaCl/(.864molNaCl+11.02)= .580

w/w .684/11.02= 3.63

To calculate the concentration of NaCl in the given solution, we can use the following formulas:

a) Mass Percentage:
Mass percentage is calculated by dividing the mass of NaCl by the total mass of the solution and multiplying by 100.

Mass percentage = (Mass of NaCl / Total mass of solution) * 100

In this case, the mass of NaCl is given as 40.0 g and the total mass of the solution is 40.0 g (NaCl) + 200.0 g (water) = 240.0 g.

Mass percentage = (40.0 g / 240.0 g) * 100 ≈ 16.7%

b) Molality:
Molality is calculated by dividing the number of moles of NaCl by the mass of solvent (in this case, water) in kilograms.

First, we need to calculate the number of moles of NaCl:
Number of moles = Mass of NaCl / Molar mass of NaCl

The molar mass of NaCl is 22.99 g/mol (atomic weight of Na = 22.99 g/mol) + 35.45 g/mol (atomic weight of Cl = 35.45 g/mol) = 58.44 g/mol.

Number of moles = 40.0 g / 58.44 g/mol ≈ 0.6851 mol

Next, we need to calculate the mass of water in kilograms:
Mass of water = 200.0 g / 1000 ≈ 0.2000 kg

Now we can calculate the molality:
Molality = Number of moles / Mass of solvent (in kg)

Molality = 0.6851 mol / 0.2000 kg ≈ 3.425 mol/kg

c) Mole Fraction:
The mole fraction of NaCl is calculated by dividing the moles of NaCl by the total number of moles of all components in the solution.

The total number of moles can be obtained by dividing the mass of each component by its molar mass and summing them up.

Number of moles of water = Mass of water / Molar mass of water
Molar mass of water = 2 * 1.01 g/mol (atomic weight of H) + 16.00 g/mol (atomic weight of O) = 18.02 g/mol

Number of moles of water = 200.0 g / 18.02 g/mol ≈ 11.10 mol

Total number of moles = Number of moles of NaCl + Number of moles of water
Total number of moles = 0.6851 mol + 11.10 mol ≈ 11.78 mol

Now, we can calculate the mole fraction of NaCl:
Mole fraction of NaCl = Number of moles of NaCl / Total number of moles

Mole fraction of NaCl = 0.6851 mol / 11.78 mol ≈ 0.0582

So, the NaCl concentration is:
a) Mass percentage: 16.7%
b) Molality: 3.425 mol/kg
c) Mole fraction: 0.0582