A mixture of K chloride and K nitrate problem

[skepticwulf]

Homework Statement

Consider a mixture of potassium chloride and potassium nitrate that is 43.2% potassium by mass. What is the percent KCl by mass of the original mixture?

Homework Equations

The Attempt at a Solution

x is the mole of KCI in the mixture
y is the mole of KNO3 in the mixture
molar mass of KCl is 74,5g/mol
molar mass of KNO3 is 101g/mol

So, 74,5x+101y=100

Also, K %mass in KCl is 39/74,5=0,5235 and K %mass in KNO3 is 39/101=0,386

So, 0,5235x+0,386y=0,432

2 unknown, 2 equations: x Solved=0,217 ...that is: 0,217x74,5=16,16gr KCl; that's %16,16 in a sample 100gr
But solution manual says it's %32.9KCl

What's wrong with my calculation?

 

[epenguin]

Homework Statement

Consider a mixture of potassium chloride and potassium nitrate that is 43.2% potassium by mass. What is the percent KCl by mass of the original mixture?

Homework Equations

The Attempt at a Solution

x is the mole of KCI in the mixture
y is the mole of KNO3 in the mixture
molar mass of KCl is 74,5g/mol
molar mass of KNO3 is 101g/mol

So, 74,5x+101y=100

Also, K %mass in KCl is 39/74,5=0,5235 and K %mass in KNO3 is 39/101=0,386

So, 0,5235x+0,386y=0,432

2 unknown, 2 equations: x Solved=0,217 ...that is: 0,217x74,5=16,16gr KCl; that's %16,16 in a sample 100gr
But solution manual says it's %32.9KCl

What's wrong with my calculation?

I think the error is in your second line and specifically in the denominators. Yours verbally sounds plausible, so write out explicitLy mass of K in KCl and mass of K in KNO₃. Oops sorry, you have. It's wrong. Mass of K is just moles of K × (atomic mass of K). OK?

 

[skepticwulf]

Thank you epenguin but I don't understand last part of your reply "Oops sorry, you have. It's wrong. Mass of K is just moles of K X (atomic mass of K). OK?"
Could you kindly elaborate on that?

 

[epenguin]

Thank you epenguin but I don't understand last part of your reply "Oops sorry, you have. It's wrong. Mass of K is just moles of K X (atomic mass of K). OK?"
Could you kindly elaborate on that?

OK, I thought I had almost given you the answer, how to calculate it anyway, and that you had gone away with that and left the thread unanswered, something that some of the HH are getting fed up with.

The X in my original answer meant ×, multiplication sign - I have only just noticed we have it in the Σ symbols list.

Just forget about percentages and just think about number of moles and number of grams. For just one component at a time, e.g. KCl.
You have x moles of KCl. How many grams of KCl is that? OK, you have that inside your first equation, using molecular mass..
Now how many moles of K are there in x moles of KCl? How many grams of K is that?

If using that you get the right answer please post at least your correct second equation here - see second line of my sig.

 

[skepticwulf]

Thank you, let me contemplate on that..