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As part of a pre-lab exercise in Chemistry, we went through the necessary calculations to identify an unknown metal in a metal carbonate. The method was gas evolution by means of hydrochloric acid (see equation below). The unknown metal was Alkali, and we had three possibilities: Lithium, Sodium, and Potassium as $\ce{M}$.

$$\ce{HCl + M2CO3 -> MCl + CO2 + H2O}$$

Using data given to us, we first converted grams of released $\ce{CO2}$ to moles. Then here was the part I was confused on. To find the molar mass of the metal carbonate, we took the mass of the sample used (the metal carbonate) and divided it by moles of $\ce{CO2}$ released, which was just calculated. The rest here on out was a little algebra. What is the reasoning behind dividing the mass of the sample by released $\ce{CO2}$? What makes it "legal"? Yes, in the balanced equation, the ratio of $\ce{M2CO3}$ to $\ce{CO2}$ was $1:1$.

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$$\ce{HCl + M2CO3 -> MCl + CO2 + H2O}$$

Since you already figured out, that there is a one-to-one ratio of carbonate to carbon dioxide, you can simply write $$n(\ce{CO2}) = n(\ce{M2CO3}).$$

With the formula for the Molar mass, $$M(\ce{M2CO3}) = \frac{m(\ce{M2CO3})}{n(\ce{M2CO3})},$$ you can simply substitute one for the other, hence $$M(\ce{M2CO3}) = \frac{m(\ce{M2CO3})}{n(\ce{CO2})}.$$

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Your equation isn't balanced though. Correct equation: $\ce{M2CO3 + 2HCl -> 2MCl + CO2 + H2O}$

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