Question

A 2.00 M solution of CaCl2 (111 g/mol) in water has a density of 1.17 g/mL. What is the mole fraction of CaCl2? Enter your answer with 4 decimal places. Hint: Start with 1.00 L of solution.

Answer 1

0.0366

Step-by-step explanation:

The problem states there is 2.00M of CaCl2. This can be re-written as 2.00 moles of CaCl2 over 1 liter of solution:
`(2.00 moles of CaCl2)/(1 liter of solution)`

What we want is the mole fraction of CaCl2 which can be written as moles of solute over total moles of solution:
`(moles of solute)/(Total moles of solution)`

As you can see, the numerator of the first equation matches the numerator of the second equation so we don't need to do anything to solve for the numerator of the second equation. Therefore let's focus on solving the denominator of the second equation.

Start by converting 1 liter of solution into grams:

`1L * (1000ml)/(1L)*(1.17g)/(1ml)` = 1,170 grams of solution

We can use the density provided to us in the problem to convert from volume units to mass units.

So we know that there are 1,170 grams of solution but since we don't know how much of that solution is CaCl2 and how much of that solution is H20, the next step would be to find the mass (in grams) of CaCl2 and then subtract that mass to the total mass of solution. The amount of solution left after subtracting the amount of CaCl2 is the amount of H20 in the solution:

`2 mols CaCl2 * (111g)/(1 mol)` = 221.96g CaCl2

1170g solution - 221.96g CaCl2 = 948.03g H20.

Next step is to convert the grams of H20 into moles:

`948.03g H20*(1 mol)/(18g)` = 52 moles of H20.

Now we have all the information we need to plug into the second equation and solve for the mole fraction of CaCl2:

`(2 moles CaCl2)/(2 moles CaCl2 + 52 moles H20)` = 0.0366

Answer 2

0.03586

Step-by-step explanation:

Given data

2M solution means 2 moles of Cacl2 in 1 L of solution.

mass of solution = 1000mL×1.17 g/mL= 1170g

mass of CaCl2= 2mole×111 g/mol =222g

mass of water= 1170-222=968g

moles of water= 968/18= 53.77 moles

mole fraction of CaCl2=
`(moles of CaCl_2)/(moles of CaCl_2+moles of water)`

mole fraction of CaCl2=
`(2)/(2+53.77)`

=0.03586