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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

Thanks in advance

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    $\begingroup$ 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? $\endgroup$ – Karl Oct 28 '18 at 10:17
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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...

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    $\begingroup$ 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. $\endgroup$ – Oscar Lanzi Oct 30 '18 at 18:41

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