The mole fraction of an aqueous solution of sodium dichromate is 0.367. Calculate the molarity (in mol/L) of the sodium dichromate solution, if the density of the solution is 1.42 g mL-1.

XNa2CrO4 = 0.367.

XH2O = 1-0.367 = 0.633
Suppose we have 1 mol of solution. That means we have 0.367 mol Na2CrO4 and 0.633 mol H2O. 0.633 mole H2O = 0.633*18 g/mol = 11.4 g H2O. g Na2CrO4 = mols x molar mass = 0.367*about 162 = about 59.5. Total mass of solution = 59.5+11.4 = about 71 grams. mass = volume x density or volume = mass/density = 71/1.42 = about 50 mL and 0.367moles/0.050 L = ??M Check my work. It's late. I've estimated so you need to clean up the numbers.

To calculate the molarity of the sodium dichromate solution, we need to know the molar mass of sodium dichromate (Na2Cr2O7).

The molar mass of Na2Cr2O7 can be calculated by adding up the atomic masses of the individual elements:
- 2 sodium atoms (Na): 2 × 22.99 g/mol = 45.98 g/mol
- 2 chromium atoms (Cr): 2 × 52.00 g/mol = 104.00 g/mol
- 7 oxygen atoms (O): 7 × 16.00 g/mol = 112.00 g/mol

Adding up these masses gives the molar mass of Na2Cr2O7:
45.98 g/mol + 104.00 g/mol + 112.00 g/mol = 262.98 g/mol

Next, we need to calculate the number of moles of sodium dichromate in the solution. The mole fraction (X) is the ratio of the moles of sodium dichromate (n) to the total moles of solute and solvent in the solution. In this case, we can assume the total moles is equal to the moles of sodium dichromate since it's dissolved in water.

So, we can write the equation:
X = n/(n + n_water)

Given that the mole fraction (X) is 0.367, we can plug in the values:
0.367 = n/(n + n_water)

Since n + n_water represents the total moles, we can rewrite the equation:
0.367 = n/total_moles

To calculate the molarity (M), we need to know the volume (V) in liters. We can obtain volume by dividing the mass of the solution by its density.

Given that the density of the solution is 1.42 g/mL, we can calculate the mass of the solution using the equation:
mass = density × volume

Since the density is given in g/mL, we need to convert the density to g/L by multiplying it by 1000 (since there are 1000 mL in 1 L):
density = 1.42 g/mL × 1000 mL/L = 1420 g/L

Now, we can solve for the volume (V) using the equation:
mass = density × volume
volume = mass/density

As we want to calculate the molarity, we need to know the moles per liter. So, we need to divide the number of moles (n) by the volume (V) in liters:
Molarity (M) = n/V

We now have all the necessary information to calculate the molarity (M) of the sodium dichromate solution. Let's break it down step by step:

Step 1: Calculate the molar mass of Na2Cr2O7:
Molar mass = 45.98 g/mol + 104.00 g/mol + 112.00 g/mol = 262.98 g/mol

Step 2: Calculate the number of moles of sodium dichromate:
0.367 = n/total_moles
n = 0.367 × total_moles

Step 3: Calculate the volume (V) of the solution in liters:
volume = mass/density = mass/1420 g/L

Step 4: Calculate the molarity (M):
Molarity (M) = n/V = (0.367 × total_moles)/(mass/1420 g/L)

Plug in the given values to calculate the molarity of the sodium dichromate solution.