0.872g sample containing only NaBr and KBr gives 1.052g AgBr. what's the % of each salt?

This is the type of problem that cannot be answered without other information.

I think you have made a typo in your problem I worked through it and I get negative numbers for the mass of NaBr and KBr. Of course that can not be. Perhaps the mass AgBr produced is 1.502 and not 1.052; that is, perhaps you transposed those numbers. Check it out.
The problem is set up this way but you will need to substitute the correct values. I have used 1.502g for mass AgBr produced.

You have two equations and two unknowns.
Let Y = grams KBr.
Let Z = grams NaBr.
Note: AgBr, KBr, and NaBr below stand for molar mass of those materials.
=======================
eqn 1 is Y + Z = 0.872
eqn 2 is Y(AgBr/KBr) + Z(AgBr/NaBr)=1.502

Solve for Y and Z which is grams of each.
Then determine % by
%KBr = (massKBr/1.502)*100 and
%NaBr=(mass NaBr/1.502)*100.

Post your work if you get stuck.

It seems like you have a tricky chemistry problem on your hands! But don't worry, I'm here to lighten the mood and help you through it.

Now, before we begin, let's address the elephant in the room - the typo in the problem. It seems that there might be an error in the given value of 1.052g AgBr. As the clever bot that I am, I suggest we consider the possibility that it should be 1.502g instead. After all, transposing numbers can happen to the best of us!

Now that we have that sorted out, let's dive into the problem. We have a mixture containing only NaBr and KBr, and we want to find the percentage of each salt.

To solve this, we need to set up two equations. Let's call the gram of KBr Y and the gram of NaBr Z. Now, please excuse my equation indigestion, but here we go:

Equation 1: Y + Z = 0.872g (the total mass of the sample)
Equation 2: Y(AgBr/KBr) + Z(AgBr/NaBr) = 1.502g (the mass of AgBr produced)

Using these two equations, you can solve for Y and Z, which will give you the gram amounts of each salt present in the sample.

Once you have the mass of each salt, you can calculate the percentage of KBr and NaBr by dividing the mass of each salt by 1.502g (or, if you're still not convinced, by the corrected mass of AgBr produced), and then multiplying by 100.

So, just plug in the numbers, do the math, and voila! You'll have the percentages of KBr and NaBr in the sample. And remember, if you get stuck along the way, I'm here to provide a little comedic relief or a shoulder to cry on (figuratively speaking, of course). Good luck!

To solve the system of equations, we can use substitution or elimination method. Let's use substitution method:

From equation 1:
Y + Z = 0.872

Solve equation 1 for Y:
Y = 0.872 - Z

Substitute this value into equation 2:
(0.872 - Z)(AgBr/KBr) + Z(AgBr/NaBr) = 1.502

Multiply through by the denominators:
0.872(AgBr) - Z(AgBr/KBr) + Z(AgBr/NaBr) = 1.502

Multiply through by KBr and NaBr to eliminate the denominators:
0.872(AgBr)(KBr) - Z(AgBr) + Z(AgBr)(NaBr) = 1.502(KBr)(NaBr)

Simplify:
0.872(AgBr)(KBr) + Z(AgBr)(NaBr - KBr) = 1.502(KBr)(NaBr)

Now, substitute the values:
0.872(187.77)(39.1) + Z(187.77)(22.99 - 39.1) = 1.502(39.1)(22.99)

Simplify and solve for Z:
0.872(7342.655) + Z(187.77)(-16.11) = 1.502(862.019)

6416.491 + Z(-2988.144) = 1295.809

Z(-2988.144) = 1295.809 - 6416.491
Z(-2988.144) = -5119.682

Z = -5119.682 / -2988.144
Z ≈ 1.711 g

Substitute this value back into equation 1 to solve for Y:
Y + 1.711 = 0.872

Y = 0.872 - 1.711
Y ≈ -0.839 g

However, since we cannot have negative masses, it means there is an error in the problem or calculation. Please double-check the values given and redo the calculations.

To solve this problem, we first need to set up a system of equations.

Let Y be the grams of KBr and Z be the grams of NaBr.

The first equation is Y + Z = 0.872g. This equation represents the total mass of the sample.

The second equation involves the amount of AgBr produced. It is given that 1.052g of AgBr is produced. However, you mentioned that there may be a typo, so we will use the value of 1.502g instead. The equation becomes:

Y(AgBr/KBr) + Z(AgBr/NaBr) = 1.502g.

Now we can solve this system of equations to find the values of Y and Z. Once we have those values, we can calculate the percent of each salt.

To find the values of Y and Z, you can use substitution or elimination. I'll use elimination in this explanation since it's a bit simpler.

Multiply the first equation by (AgBr/KBr) to get rid of Y in the second equation:

(Y + Z)(AgBr/KBr) = 0.872g(AgBr/KBr)
Y(AgBr/KBr) + Z(AgBr/KBr) = 0.872g(AgBr/KBr).

Now the second equation becomes:

0.872g(AgBr/KBr) + Z(AgBr/NaBr) = 1.502g.

Subtract this equation from the previous one to eliminate Z:

Y(AgBr/KBr) + Z(AgBr/NaBr) - (0.872g(AgBr/KBr) + Z(AgBr/NaBr)) = 0.872g(AgBr/KBr) - 1.502g.

Simplifying this gives:

Y(AgBr/KBr) - 0.872g(AgBr/KBr) = -0.63g.

Factor out (AgBr/KBr):

(AgBr/KBr)(Y - 0.872g) = -0.63g.

Now divide both sides by (AgBr/KBr) to solve for Y:

Y - 0.872g = -0.63g / (AgBr/KBr).

Simplifying further, we get:

Y = -0.63g / (AgBr/KBr) + 0.872g.

Now substitute this value of Y back into the first equation to solve for Z:

(-0.63g / (AgBr/KBr) + 0.872g) + Z = 0.872g.

Simplifying this equation gives:

Z = 0.872g - (-0.63g / (AgBr/KBr) + 0.872g).

Now that we have the values of Y and Z, we can calculate the percentage of each salt.

To find the percent of KBr, divide the mass of KBr by 1.502g (or the corrected mass of AgBr), and then multiply by 100:

%KBr = (Y/1.502g) * 100.

To find the percent of NaBr, divide the mass of NaBr by 1.502g (or the corrected mass of AgBr), and then multiply by 100:

%NaBr = (Z/1.502g) * 100.

Plug in the values of Y and Z into these equations to calculate the percentages of each salt.

Remember to be careful with the calculations and check for any errors or typos in the given values before proceeding.