5 replies to this topic

[caruga]

Say I have potassium chloride and sodium chloride and want to make a combined solution where there is 52 parts sodium for every 48 parts potassium.  I want to make 100 grams of this.  Since they don't have the same molecular weight I can't just have 52 grams of sodium chloride, 48 grams potassium chloride.  So how do i work this out?  If someone could explain how they arrive at the solution I'd appreciate it.

[Darryl]

NaCl: 58.44 g/mol

KCl: 74.5513 g/mol

 

Desired ratio NaCl (g) /KCl (g) = (52/48) * (58.44/74.5513) = 0.849 

Alternatively, KCl (g) / NaCl (g) = 1.178

 

100 * 1 / (1 + 1.178) = 45.91 g NaCl

The balance (100 * 1.178 / (1 + 1.178)) = 54.09 g KCl

[caruga]

NaCl: 58.44 g/mol

KCl: 74.5513 g/mol

 

Desired ratio NaCl (g) /KCl (g) = (52/48) * (58.44/74.5513) = 0.849 

Alternatively, KCl (g) / NaCl (g) = 1.178

 

100 * 1 / (1 + 1.178) = 45.91 g NaCl

The balance (100 * 1.178 / (1 + 1.178)) = 54.09 g KCl

 

I was expecting  it to involve calculating off of the mass of sodium and potassium as well.  Is one mole of sodium and one mole of potassium containing an equal number of sodium and potassium particles?

Just to test if i understand the principle then (I might just be copying without any real understanding) I'll try a different goal:

If I want three parts sodium to two parts potassium, I do:

(66/33) * (58.44/74.5513) = 0.7839

0.7839/99*100 = 0.792

100 * 1 / (1+0.792) = 55.8035 sodium chloride?  And 44.197 potasium chloride?  Or did I go wrong somewhere?

[niner]

caruga, do you want the ratio to be number of particles (moles) or mass of Na per mass of K?  Darryl did it in such a way that you'd get the mole ratio, which is how I'd expect it to be, but I don't really know what you're going to do with it, so it's not entirely obvious what you'd want.

 

If you want 3 moles Na to 2 moles K, wouldn't it be  (3/2) * (58.44/74.5513) = 1.176 ?

 

then, X g KCl + 1.176 X g NaCl = 100 g mixture.   Solve that for X, and you get  X = 100/2.176 = 45.95.  Therefore, you'd need 45.95 grams of KCl, and the balance in NaCl.  That's perilously close to what you got, which makes me think that one of us did something wrong, since I started with a molar ratio of 1.5 Na/K, and you started with 2.0 Na/K.  It seems like our masses should be further apart.

[caruga]

caruga, do you want the ratio to be number of particles (moles) or mass of Na per mass of K?  Darryl did it in such a way that you'd get the mole ratio, which is how I'd expect it to be, but I don't really know what you're going to do with it, so it's not entirely obvious what you'd want.

 

If you want 3 moles Na to 2 moles K, wouldn't it be  (3/2) * (58.44/74.5513) = 1.176 ?

 

then, X g KCl + 1.176 X g NaCl = 100 g mixture.   Solve that for X, and you get  X = 100/2.176 = 45.95.  Therefore, you'd need 45.95 grams of KCl, and the balance in NaCl.  That's perilously close to what you got, which makes me think that one of us did something wrong, since I started with a molar ratio of 1.5 Na/K, and you started with 2.0 Na/K.  It seems like our masses should be further apart.

 

I wouldn't mind knowing both, but i'm more interested in molar ratio.

 

I'm honestly a bit confused as to why the result are similar.  1.5 was the ratio I wanted, I just goofed there.  And the /99*100 upscaling was probably misguided as well.

[niner]

Well, if you want a 1 Na to 1 K mole ratio, then the masses are 58.44 / 74.5512.  You can scale that by any Na / K ratio that you want just by multiplying.  I think you have that much pretty well in hand, but I think that the algebra (X g KCl + 1.176 X g NaCl = 100 g mixture; solve for X) is where the problem is.  If you want a 1 NaCl to 1 KCl mass ratio, then the masses are just 1:1.  If you want an equal mass of sodium and potassium, without considering the mass of the Chloride, then you have to consider the mass of Na and K separately and get the fraction of each salt that is Na or K.

 

Na = 22.99 g/m

K = 39.10 g/m

Cl = 35.45 g/m

 

NaCl = 58.44 g/m

KCl = 74.55 g/m

 

To convert the ratio of masses of the Na and K atoms to ratios of the chloride salts, I'll start with a 1:1 Element mass ratio, and multiply by conversion factors that each equal unity, but that change the units to the salt mass ratio:

 

1g Na / 1g K * (1m NaCl / 22.99 g Na) (58.44 g NaCl / 1m NaCl) * (39.10g K / 1 m KCl) * (1 M KCl / 74.55 g KCl) = (39.10/22.99) * (58.44/74.55) = 1.33 g NaCl / 1 g KCl

 

That's kind of ugly, but all the units cancel and you end up with the ratio of masses of the two salts that give you equal masses of the positive ions.  (I'm not sure why you would want this...) What are you using this for, anyway?