Let X = mass K2CO3
and Y = mass Li2CO3
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eqn 1:
X + Y = 0.500g
eqn 2:
(#Eq X) + (#Eq Y) = 0.0075 or
equivalents K2CO3 + equivalents of Li2CO3 = 0.0075 or
(X/69) + (Y/37) = 0.0075
0.01449X + 0.02703Y = 0.0075
We can solve for Y from equation 1 by
X + Y = 0.50
Y = 0.50-X and substitute that into equation 2.
(0.01449X) + 0.02703(0.50-X) = 0.0075
0.01449X + 0.01352 - 0.02703X = 0.0075
0.01449X - 0.02703X = 0.0075-0.01352
-0.01254X = -0.00602
X = 0.48g = mass K2CO3
Then X + Y = 0.50 and
0.48 + Y = 0.50 and
Y = 0.02 mass Li2CO3
%K2CO3 = (mass K2CO3/mass sample)*100 = 96%
%Li2CO3 = (mass Li2CO3/mass sampl)*100 = 4%.