Elliott Writes…

The following questions will be covered here:

1) What is dry ice, why is it called ‘dry’, and ‘decompressed’?

2) What volume of carbon dioxide gas (at STP) is contained in a gram of this stuff?

3) If that volume of gas were confined to a 2-liter bottle, how much pressure would be inside the bottle?

4) How can the pressure-breaking point of various containers be determined with dry ice?

Question 1: What is dry ice, why is it called ‘dry’, and ‘decompressed’?

Dry ice is a frozen-solid form of the gas CO₂, Carbon Dioxide. Carbon dioxide does not have a liquid form, and sublimes directly between gas and solid states. The ice is made by collecting CO₂ gas in a container, and quickly decompressing the chamber through small valves. When this occurs, the gas leaves at such a fast velocity that portions of the gas freeze near the openings, and thus the term ‘decompressed’. A piece of dry ice is certainly ‘compressed’ by most definitions, and the term ‘decompressed’ is largely misleading, as it only pertains to a method used to create the gas. Because a large volume of gas (at STP — see below for more information about STP) is made to fit into such a comparatively small space, people think of this as compressed. However, given the state-change (gas to solid), I’m not sure if ‘compressed’ is the proper term either.

Question 2: What volume of carbon dioxide gas (at STP) is contained in a gram of this stuff?

To determine this, we must first define a few things.

a) STP - standard temperature and pressure. Standard temperature is defined as 0˚C (273.15 Kelvin), and standard pressure is defined as 1 atm.

b) 1 atm (atmospheric unit) equals 14.7 psi, or 760 torr (mm Hg).

c) Formulas are given in molar or formula quantities - not mass. So 1 mol of CO₂ gas has 1 mol of carbon for every 2 mol of oxygen. The point being, percent composition by mass or volume is different than the molar (or atomic) composition ratio presented in the formula (CO₂).

d) The mass of a substance does not change in a contained environment with any physical change (pressure, temperature, volume, state, etc). So, an ice cube’s weight doesn’t change when it is melted.

e) 1 mol of any gas, at STP, has a volume of 22.4 Liters. (This is a ratio, which can be used to convert between volume and mols of any gas.) Additionally, the volume of 1 mol of any gas at 25˚C, 1 atm, is 24.5 Liters. This is more realistic for some calculations.

With all this information, here is the process to determine how much gas, at STP, 1 gram of dry ice contains.

First, the molar weight of CO₂ must be calculated. Simply add the molar weight of each part of the formula (don’t forget — two mol of oxygen) together.

C:    12.01g/mol    x1    12.01g
O:    16.00g/mol    x2    32.00g
total:          	  44.01g / mol CO2

The conversion to volume (liters) requires mols, rather than mass (because gases ’spread’ out on a per-particle basis, mostly independent of mass). So multiply a given mass of dry ice times the molar mass ratio of CO₂:

And now, how many liters is 0.023 mol CO₂ gas at STP?

So 1 gram of CO₂ (solid or gas — state is independent of mass) will use 0.525 Liters, if the pressure is kept at 1ATM, and volume is allowed to expand (such as dry ice subliming in an open room). Because this was calculated using straight multiplication, it’s easy to see that 1Kg of CO2 will use 515 Liters at STP. (About $.25 worth, at Sparkling Carbonic.)

Question 3: If that volume of gas were confined to a 2-liter bottle, how much pressure would be inside the bottle?

So let’s say that rather than allowing the gas into an open room, the dry ice is contained, in a sealed, non-expanding container.

To make things interesting, this calculation will be made with 20 grams of CO₂.

The combined gas law states:

Where P is pressure (in any unit you like, just stay consistent), V is volume (typically in Liters, though any consistently-used unit should be fine), and T is temperature (use the Kelvin scale to avoid negative values). Assume that Temperature is held constant (though we know it isn’t really — but it is for our purposes). Set the initial volume and pressure to the calculated value for the volume of 20 grams CO₂ at STP, and set the ending volume at 2 Liters (calculate the pressure value).

20g of CO₂ is equal to 0.454 mols. Times 22.4 mol per 1 Liter gives a volume of 10.17 Liters. Catch that? 20 grams of CO₂ has a volume of 10.17 Liters, at STP.

10.17 Liters without restricting volume. So what if volume is restricted to 2 Liters? How much pressure would be inside that vessel?

Eliminating temperature from the combined gas law, this can be easily calculated:

20g of CO₂(g) contained in a 2 Liter bottle (one that doesn’t break or expand) will be at a pressure of 5.085 atm, or 74.749 psia. If you’re comparing this to tire pressure (psig), remember that tire pressure psi is actually off by 14.7 psi (1 atm), because tire pressure is rated against STP. Applying Dalton’s law of Partial Pressures, add one atm to account for the air present in the bottle before the experiment. Leaving a total of 6.085 atm, or 89.45 psia (104.2 psig).

Question 4: How can the pressure-breaking point of various containers be determined with dry ice?

Obviously, a normal soda bottle is going to bust way before this pressure is reached. So the question is, can this threshold be calculated? Yes, it can!

If the CO₂ ice is massed before the bottle is shattered, and the remaining ice, after the bottle shatters, is massed, this difference, converted from grams to moles to liters to pressure, is the shattering threshold.