First, let's derive the right equations for this problem. Let x be the mass of NaCl and y be the mass of KCl. Then the total mass equation for the mixture is:
x + y = 4.000
Since NaCl and KCl form equivalent masses of AgCl with silver nitrate, we can use the following relationship for the mass of AgCl formed from each component separately:
AgCl_mass(NaCl) = (x / mass_NaCl) * mass_AgCl = (x / 58.5) * 143.5
AgCl_mass(KCl) = (y / mass_KCl) * mass_AgCl = (y / 74.5) * 143.5
The sum of these two masses will be equal to the total mass of the AgCl precipitate:
(143.5x/58.5) + (143.5y/74.5) = 8.5904
Now we have our system of equations:
1) x + y = 4.000
2) (143.5x/58.5) + (143.5y/74.5) = 8.5904
We can solve for x and y by solving for one of the variables and then plugging the solution back into the other equation. Let's solve for x in equation 1:
x = 4.000 - y
Now plug this solution for x back into equation 2:
(143.5(4.000 - y)/58.5) + (143.5y/74.5) = 8.5904
Solve for y first:
y ≈ 1.9893 g (use more significant figures since this is an intermediate step)
Now plug the value of y back into the equation for x:
x = 4.000 - 1.9893
x ≈ 2.0107 g (use more significant figures since this is an intermediate step)
Now calculate the mass percent of each component in the mixture:
%NaCl = (2.0107 / 4.000) * 100 = 50.27%
%KCl = (1.9893 / 4.000) * 100 = 49.73%
The mass percent of each component in the mixture is approximately 50.27% NaCl and 49.73% KCl.
A sample of a mixture containing only sodium chloride (NaCl) and potassium chloride (KCl) has a total mass of 4.000g. When this sample is dissolved in water and excess silver nitrate is added a white precipitate (AgCl) forms. After filtration and drying, this precipitate had a mass of 8.5904g. Calculate the mass percent of each component in the mixture.
--58.5x + 74.5y = 4
143.5 (x+y) = 8.5904
Using system of equations,
x = 0.028 y=0.031
NaCl = 58.5*0.028 / 4 *100 = 43 %
KCl = 74.5 * 0.031 / 4 *100 = 57 %
Is this right?
Your values for %NaCl and %KCl are close (within 1%) but for the life of me I can't figure out what you did?
What is X and what is Y? I wonder if your equations gave you close to the correct value by chance. I know you solved two equations simultaneously. Also, since 4.000 is to 4 places and 8.5904 is to 5 places, I think you should use more signifivant figures than you have for NaCl, KCl, and AgCl.
1 answer
0 answers