A chemistry question about Stoichmetry?

Question

A sample containing NaCl, Na2SO4and NaNO3 , gives the following analysis in percent by mass : Na =32.08%, O=36.01% , Cl= 19.51%. calculate the percent by mass of each compound n the sample.

Answer 1

using molar masses, we can learn

19.51 g Cl @ 58.44 g NaCl / 35.45 g Cl =

"almost an answer":  32.16 grams NaCl

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32.16 g NaCl - 19.51 =  12.65 g Na in the NaCl

32.08 g Na - 12.65 g Na in NaCl = 19.43 g Na in the other two ...

and  with "X" = moles  Na2SO4 , & "Y" = moles NaNO3:

19.43 g Na = (X mol) (45.98g Na/ mol Na2SO4)  +  (Y mol)(22.99 g Na / mol NaNO3)

19.43g = 45.98X + 22.99 Y   (aka equation A)

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however with a total of 36.01 g of oxygen in the other two...

and with "X" = moles  Na2SO4 , & "Y" = moles NaNO3:

36.01 g O  = (X mol) (64.00 g O/ mol Na2SO4)  +  (Y mol)/(48.00 g O/ mol NaNO3

36.01g = 64X  & 48Y

therefor Y = (36.01 - 64 X) / 48  (aka equation B)

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equation A :

19.43g = 45.98X + 22.99 Y

substituting equation B into equation A:

19.43g = 45.98X + 22.99 (36.01 - 64 X) / 48

multiplying all by 48:

932.64 = 2207.04X + 22.99 (36.01 - 64 X)

which gives:

932.64 = 2207.04X + 827.87  - 1471.36 X)

rearranging gives:

104.77  = 735.68X

solving:

X = moles of Na2SO4 = 0.1424

0.1424 moles Na2SO4 @ 142.04 g/mol =

for another "almost an answer": 20.23 grams Na2SO4

====================

now back to the finding the Na in another compound:

0.1424 moles of Na2SO4 @ (2mol Na)(22.98 g/mol) Na / mole Na2SO4 =

6.55 grams of Na are in the Na2SO4

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32.08 g Na total - 6.55 g Na in Na2SO4 - 12.65 g Na in NaCl =

12.88 g Na are in NaNO3

so lets use it & molar masses, to get the grams of NaNO3:

12.88 g Na @ (84.99 g/mol) NaNO3 / 22.98 g Na=

your last "almost an answer": 47.64g NaNO3

======================================...

to summarize, we found:

47.64 grams NaNO3

20.23 grams Na2SO4

32.16 grams NaCl

which totals 100.0 grams of compounds

so your final answers are:

47.64 % NaNO3

20.23 % Na2SO4

32.16 % NaCl

well there goes an hour, now back to putting my daughter's transmission back into her car