This problem, is describing two scenarios, the first one, a reaction between potassium carbonate and nitric acid, and also this very same acid with sodium carbonate. In addition, it is asked to set up two equations whereby you can get the grams of nitric acid needed to react with the unknown grams of both carbonates.
In this case, we can start off by designating the unknown mass of potassium carbonate as X and that of sodium carbonate as Y, so that we will be able to provide a reliable answer. Next, we write the corresponding chemical equations that take place:
K2CO3 + 2HNO3 --> 2KNO3 + H2O + CO2
Na2CO3 + 2HNO3 --> 2NaNO3 + H2O + CO2
After that, we can set up the conversion by considering the following calcultion track:
g Carbonate --> mol Carbonate --> mol HNO3 --> g HNO3
The conversion from grams to moles involve the carbonates' molar mass and the conversion from moles of nitric acid to grams, its molar mass well. In addition, we need the 1:2 mole ratio of the carbonates to nitric acid that it is evidenced in the reaction.
Therefore, the resulting equations that can be set up are shown as follows:
[tex]X g K_2CO_3 *\frac{1mol K_2CO_3 }{138.2 gK_2CO_3 } \frac{2molHNO_3}{1molK_2CO_3 } *\frac{63.1gHNO_3}{1molHNO_3} \\\\Y g Na_2CO_3 *\frac{1mol K_2CO_3 }{105.99 gK_2CO_3 } \frac{2molHNO_3}{1molNa_2CO_3 } *\frac{63.1gHNO_3}{1molHNO_3}[/tex]
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