# CO2 Recipe

Most people can figure out the basic reaction for baking soda and vinegar by looking it up online. Also the math for the stoichiometry is pretty simple and again can be found online. However, translating from that to a specific amount of CO2 can be a bit tricky. You need to start out by picking the amount of CO2 you want to create. In my case I was trying to fill a nearly spherical  party balloon to it’s full size. When fully inflated the balloon had a circumference of about 87 cm or 0.87 meters. Then I used the following equation to find the total amount of gas I wanted:

$\frac{4}{3}\pi&space;\left&space;(&space;\frac{circumference}{2\pi&space;}&space;\right&space;)^{3}=volume$

In my case this came out to be 0.0111 m3 converting to liters in this case is simply multiplying by 1000 giving me 11.1 liters as my target volume. This is convent because it’s about half a mole of gas. It happens that any gas at standard temperature (0 c) and atmospheric pressure will fill up 22.4 liters. Just about twice as much as I need. Now while I assume you will not be doing this at freezing temperature but difference in volume for room temperature is only 2 more liters. So half a mole of gas will give me somewhere between 11 and 12 liters of gas. But I will assume that the reaction won’t proceed perfectly and there will be some losses, as such making the recipe for half a mole is about right to fill up the balloon.

Next We need to look back at the stoichiometry to figure out what the conversion factor will be for the other ingredients.

$7&space;\left&space;(C_{2}H_{4}O_{2}&space;\right&space;)&space;+&space;8&space;\left&space;(NaHCO_{3}&space;\right&space;)&space;=&space;8&space;\left&space;(NaC_{2}H_{2}O_{2}&space;\right&space;)&space;+&space;10&space;\left&space;(H_{2}O&space;\right&space;)&space;+&space;6&space;\left&space;(CO_{2}&space;\right&space;)$

That coefficient of 6 next to the CO2 means that this equation would produce 6 moles of gas, but we want only half a mole. So we need a conversion factor. In other words what times 6 is equal to 0.5? Putting on our algebra hat we can figure out that the conversion factor is 0.05/6 or 0.833. That is this is the number to multiply everything by to find out the number of moles needed.

$0.5833&space;\left&space;(C_{2}H_{4}O_{2}&space;\right&space;)&space;+&space;0.6666&space;\left&space;(NaHCO_{3}&space;\right&space;)&space;=&space;0.6666&space;\left&space;(NaC_{2}H_{2}O_{2}&space;\right&space;)&space;+&space;0.8333&space;\left&space;(H_{2}O&space;\right&space;)&space;+&space;0.5&space;\left&space;(CO_{2}&space;\right&space;)$

From these values we can calculate the number of grams needed for the reaction. That is we multiply the coefficient (0.5833 for vinegar and 0.666 for baking soda) times the molar mass of the substance (60.05 g/mol for vinegar and 84.00 g/mol for baking soda). For baking soda it’s a pretty simple step to measure out an amount by weight and then convert that to an easy measurement system. For me the 56 grams I wanted for Baking Soda was a little over 2 tablespoons (this can vary depending on the density of you baking soda and how pure it is).

However, the Vinegar presents a problem, it has been diluted. That is a whole lot of water is in there with it. Typical grocery store vinegar is at about 5% acidity, this means that the for every 100 grams of Vinegar solution only 5 of those grams are actual acetic acid molecules, the rest is water. So in our case we wanted to have 35 grams of acetic acid, but that means we need way more than that in vinegar. Since we know that 5 grams of acetic acid is in every 100 grams of solution all we need to find is how many “5’s” we need. So divide 35 by 5 and this gives us 7. That is 7 times the 100 grams of solution is the total amount of solution we need or 700 grams. You could choose to measure this out by weight but it’s a bit quicker to just note the fact that 1ml of water id defined at a mass of 1 g. Since the vinegar solution is nearly all water we can assume the density is the same and this leaves us with a simple  1 to 1 ratio. That is, 700 g is 700 ml. From here it’s a simple conversion to cups, which turns out to be about 2.9 or nearly 3 cups of vinegar.

So the final recipe for CO2 is:

2 tbsp baking soda
3 cups White Vinegar (5% acidity)

Mix in container with apparatus to capture the escaping gas. Yield: between 10-11 liters of gas.