Density problem...DESTROYER 2010 #81

[Cofo]

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I am not understanding the math on this. It's so frustrating...I've spent the last 40 minutes on this one F***ING PROBLEM.

A solution of LiCl has a density of 1.13 g/cm^3. If the solution is 20% by weight LiCl, which is the molarity?

The answer is supposed to be about 5.3 M

 

[needzmoar]

I am not understanding the math on this. It's so frustrating...I've spent the last 40 minutes on this one F***ING PROBLEM.

A solution of LiCl has a density of 1.13 g/cm^3. If the solution is 20% by weight LiCl, which is the molarity?

The answer is supposed to be about 5.3 M

The density allows you to relate the solution's mass to volume. It means that for every mL of the solution, the solution has a mass of 1.13g, got it? good.

The percent by weight is a ratio of the solute's mass to solution's mass. Less assume the solution weighs 100g that means the solute's mass is 20g

Now get the moles of LiCl --> 20/42.3 = .471 moles of LiCl

And since we assumed the solution's mass was 100g we get to use the density to figure out the solution's volume. (100g)(1mL/1.13g) = 88.5 mL

Now that you have moles solute and volume of solution you can get molarity. Don't forget to convert mL to L

 

[RalphMouth]

For these problems, it's usually best to just assume 100g you could use any number you want as long as the ratios are correct) of the total for easier calculation purposes. Since we know that LiCl is 20 percent by weight of the solution. Weight of LiCl = 20 g. MW of LiCl= 42.5

20/42.5 = 0.47 mol

Since we assumed we have 100 g of total solution, we simply set up a ratio of
1.13 g/ 1 mL = 100g/x mL. A cubic cm = a mL. Solve for the volume of the solution assuming 100 g and you get 88 mL.

0.47 mol / .088 L = ~ 5.3 M