Basic chemistry question

[Sicilian]

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A mixture of NaCl and KCl weighs 5.4892 g. The sample was dissolved in water and reacted with an excess of silver nitrate in solution. The resulting AgCl weighs 12. 7052 g. What was the percentage of NaCl in the mixture?


Answer: Two parallel reactions,

(I) NaCl + AgNO3 ---> AgCl + NaNO3

(II) KCl + AgNO3 ---> AgCl + KNO3

And then:

x + y = 5.4892 g

and (x/58.443 g/mol) + (y/74.551 g/mol) = 0.088649 mol

From which x = 4.0624 g and %NaCl = 74.01 %

According to the book, the "conservation of Cl atoms requires that the number of moles of AgCl formed equals the sum of the number of moles of NaCl and KCl." I want to know, how can that be proved? It seems to me that thats the case only if the NaNO3 and KNO3 are ignored. In other words, if the two parallel reactions are written like this:

(I) ab + xycd = mb

(II) fb + xycd = mb

ab will equal fb which means that the moles of NaCl + KCl will equal the moles of silver chloride. But if I write the parallel reactions like this:

(I) ab + cd = cb + ad

(II) zb + cd = cb + zd

Either zb has to equal ab or ad has to equal zd so that moles of Nacl + moles of KCl = moles of AgCl. Neither of which I can prove. In other words, if I include the NaNO3 and KNO3 the proof doesn't work. So I am guessing I can ignore the NaNO3 and KNO3. But how is that possible?

 

[Hurricane95]

Remember your rules for solubility...all nitrates are soluble. Initially you have NaCl and KCl in water. Then silver nitrate is added. I always look at all the possible combinations of salts that could be formed and then consider which ones are/aren't soluble. Nitrates are all soluble, so forget about nitrate...it's like its not even there. That leaves you with 3 cations (Na+, K+ and Ag+) and only one anion, Cl-. Well you know NaCl and KCl will not precipitate, but AgCl will. Since they are telling you that silver nitrate is added IN EXCESS (very important), you know you have a silver ion for every chloride ion. This doesn't have to be proved mathematically or anything, you are making things way more complicated than they have to be for the MCAT. Silver chloride precipitates. It will keep precipitating until one of the ions runs out. Since silver is in excess, chloride will run out first. Hence all of the chloride present in AgCl must equal the initial chloride from the two salts. Since they are all single-valent, moles NaCl + moles KCl = moles AgCl.

 

[Sicilian]

Thank you. I understand now.

 

[Mister Pie]

Is this from an MCAT book? It seems a bit involved for a stand-alone question.

 

[Sicilian]

No, its from "Schaum's Outline of College Chemistry."

 

[Will Hunting]

No, its from "Schaum's Outline of College Chemistry."

i used that book. it was good practice as you can see.