Baking Soda + Citric Acid + Water = CO2, how much though? [closed]

Question

Baking soda (sodium bicarbonate) + citric acid react when mixed with water to form some amount of carbon dioxide gas ($\ce{CO2}$). I am trying to determine what percentage of the products is carbon dioxide: in other words, how much does reaction make?

Answer 1

I'm not sure what you mean by 90% and 10%. If you mean 90% yield (i.e. 90% or more of the bicarbonate ions in sodium bicarbonate will become carbon dioxide), then yes, that will happen if there is enough acid. How much is enough acid? We'll get to that in a minute. If you mean something else, like 90% of the mass of the components will become carbon dioxide, then that probably will not happen.

Let's look at why 90% of the mass of products is not carbon dioxide.

Bicarbonate anions react with protons from acid to produce carbonic acid, which decomposes to form carbon dioxide:

$$\ce{H+ + HCO3- -> H2CO3 -> H2O + CO2}$$

Let's start with a gram of sodium bicarbonate. How many bicarbonate ions are present? The molar mass of sodium bicarbonate is $84.0066\mathrm{\ g/mol}$, where a mole (mol) is a quantity equal to the number of carbon-12 atoms in 12 grams of carbon-12 or an Avogadro's number $(6.022\times 10^{23})$ of things. Atoms and molecules are very small, and the numbers of them in macro measurements are large.

So we have

$$\mathrm{1.00\ g \times \dfrac{mol}{84.0066\ g}= 0.0119\ mol}$$ $$\mathrm{0.0119\ mol \times \dfrac{6.022\times 10^{23}}{mol}=7.17\times 10^{21}\ molecules}$$

Let's stick with the mole unit since it gives us easier to conceptualize numbers.

The molar mass of carbon dioxide is $\mathrm{44.01\ g/mol}$, so if all of the bicarbonate ion in sodium bicarbonate is converted into carbon dioxide, we will get $\mathrm{0.0119\ mol}$ of carbon dioxide which is

$$\mathrm{0.0119\ mol \times \dfrac{44.01\ g}{mol}=0.524 \ g}$$

So 1.00 gram of sodium bicarbonate will product 0.524 grams of carbon dioxide. We have not even accounted for the citric acid yet. Citric acid is $\ce{H3C6H5O7}$, and it is tempting to think that some of those carbon and oxygen atoms in that molecule might become molecules of carbon dioxide. They can, but not in a reaction with sodium bicarbonate (acid-base). If you react citric acid with oxygen (combustion), then you can produce carbon dioxide.

How much acid?

Citric acid serves as a proton source - in fact it has three acidic protons. That means in theory, each molecule of citric acid can donate three protons to convert three bicarbonate anions into carbon dioxide:

$$\ce{H3C6H5O7 + 3HCO3- -> C6H5O7^3- + 3H2O + 3CO2}$$

However, those three acidic protons are not equal (and the reason for that would make a great follow-up question). Two of the protons are more acidic than carbonic acid, and the third one is slightly less acidic than carbonic acid. In theory, since carbonic acid decomposes into carbon dioxide, which escapes from solution, we can count on Le Châtelier's principle to pull even that third proton. However, in practice, we might not want to wait around. Let's use one equivalent of citric acid per two equivalents of sodium bicarbonate:

$$\ce{H3C6H5O7 + 2HCO3- -> HC6H5O7^2- + 2H2O + 2CO2}$$

So, to figure out how much citric acid (molar mass $\mathrm{192.12\ g/mol}$) we need, we have to do some calculations. Remember that 1 gram of sodium bicarboncate is 0.0119 moles, and we need 0.5 moles of citric acid for every mole of bicarbonate:

$$\mathrm{0.0119 \ mol\ bicarb\times \dfrac{1\ mol\ CA}{2\ mol\ bicarb}\times\dfrac{192.12\ g\ CA}{1\ mol\ CA}=1.14\ g\ citric\ acid}$$