I have a question involving a mole calculation which I was able to answer but took me a whole page. Whats the most efficient way of answering it? [closed]

A 10.00g, mixture of potassium carbonate and potassium hydrogen carbonate is heated to constant mass. The final mass was found to be 8.90g. calculate the % composition of the original mixture.

My values were 35.5% KHCO3 and 64.5% K2CO3

• Well, show your calculation and we show you how to simplify it. Or we can start with your ansatz. Two givens, two unknowns, what are the equations? – Karl Oct 28 '18 at 10:17

As @OscarLanzi noted $$\ce{K2CO3}$$ does not decompose when heated. Also when heated $$\ce{KHCO3}$$ decomposes to $$\ce{K2CO3}$$.

$$\ce{K2CO3 ->[\Delta] K2CO3}$$ $$\ce{2KHCO3 ->[\Delta] K2CO3 + CO2 ^ + H2O ^}$$

MW $$\ce{K2CO3}$$ = 138.205
MW $$\ce{KHCO3}$$ = 100.115

$$x$$ = mass $$\ce{KHCO3}$$

$$\dfrac{200.230-138.205}{200.230} =\dfrac{10.00 - 8.90}{x} =\dfrac{1.10}{x}$$

$$x = \dfrac{200.230\times1.10}{62.025} = 3.55$$

% $$\ce{KHCO3}$$ = $$\dfrac{3.55}{10.00}\times 100\% = 35.5\%$$

You must write really really large...

• Purely documentation: The reference to me is in a now deleted answer. That answer originally assumed that potassium carbonate decomposes to the oxide upon heating; but except for lithium, alkali metal oxysalts do not really do that. Potassium carbonate should be considered stable. – Oscar Lanzi Oct 30 '18 at 18:41