What is the mass of a liter of solution?

[IntegrateMe]

A solution of KCl has a density of 1.011 g/mL and has a concentration of 0.273 M. What is the molality of the solution? The molar mass of KCl is 74.5513 g.

So first I got g of KCl solute:

.273 (m) * 74.5513 (g/m) = 20.35 g

Total mass of solution = 1020.35g (since 1000g solvent per .273m solute).

Now density = mass/volume
Thus, volume = mass/density:

V = 1020.35 (g) / 1.011 (g/ml) = 1009 mL or 1.009 L

Now, molarity = moles/volume

So, M = .273/1.009 = .271

However, the accepted solution says .276 and does the problem differently, so I'm having trouble understanding if this is the correct or incorrect way of doing things.

Thank you!

 

[chemisttree]

By inspection, I see that a liter of solution must weigh 1011g yet you have 1020.35g using logic that escapes me. You also show that 1000g of solution must have 0.273 moles of KCl ("since 1000g solvent per .273m solute") yet the definition of MOLARITY is M = #moles/L. You are also redefining the concentration by forcing the volume to be 1.009 L yet assuming that this volume must also contain 0.273 moles of KCl.

You seem to be confusing molality with molarity.

 

[IntegrateMe]

Why must a liter of solution weigh 1011 g?

 

[Borek]

What is the density definition?

 

[IntegrateMe]

OK, so 1.011 (g/mL) = mass (g)/1000 (mL)

Correct?

 

[IntegrateMe]

Ah, chemisttree, you were right. Molality and molarity -__-

Thank you!

 

[IntegrateMe]

Can someone explain why the solution weighs 1011 g?

If I have 1000 g of solvent and 20.35 g of solute, why isn't the weight 1020.35?

 

[Borek]

Can someone explain why the solution weighs 1011 g?

If I have 1000 g of solvent and 20.35 g of solute, why isn't the weight 1020.35?

You have 20.35 g of solute, but you don't have 1000 g of solvent.

However, you have 1L of the solution of density 1.011 g/mL. That's all you need to know to calculate the solution mass.

And to move a step further - mass of solvent is not 1000 g, but mass of the solution minus mass of the solute.

 

[chemisttree]

OK, IngetrateMe... now you are starting to understand the true nature of this problem. What you need to further realize is that 1.011 g/mL is the same thing as 1011 g/L. The molarity (M) is defined by #moles KCl/L. So, how many moles of KCl are in that liter of solution of mass 1011g (mass of solvent + mass of solute)? That answer is given by the molarity which was given to you... 0.273 M or 0.273 moles KCl per liter. You can now calculate the number of moles in a liter (or 1000 g, right?).

All that remains is to find the mass of a liter of solution and Bob's your Uncle...