Eight grams of liquid carbon dioxide, sealed under its own pressure, turn into more than four litres of gas in a few milliseconds. This pack is the chemistry of that moment. Molar mass, moles, the ideal gas law, states of matter, and why we keep the cartridges out of the sun.
Work out the molar mass of CO₂ and convert a mass of gas into moles and molecules.
02
Use pV = nRT to find the volume that 8 g of CO₂ takes up at room conditions.
03
Describe the change of state inside the cartridge (liquid to gas) in terms of particles, and explain the frost on a fired cartridge.
04
Explain why pressure rises with temperature and why teams store cartridges at a steady, cool temperature.
02From the Nightmare car
The cartridge on the back of every STEM Racing car holds 8.0 g of CO₂. Most of it is liquid, because at room temperature CO₂ turns to liquid under about 57 bar of its own vapour pressure. When the launcher pin pierces the seal the pressure drops, the liquid boils almost instantly, and the expanding gas leaves through the nozzle. We noticed two things at the track this season. Fired cartridges come back covered in frost, and cars launched from a cartridge that had been sitting in the afternoon sun were less consistent. Both are chemistry.
Fig. 6 The cartridge holds CO₂ as a liquid under its own vapour pressure. Opening the seal drops the pressure below the boiling point, so the liquid boils and expands more than 400 times by the time it reaches atmospheric pressure.
03Core idea
From grams to moles to molecules
M(CO₂) = 12.01 + 2 × 16.00 = 44.01 g/mol · n = m / M · N = n × 6.022 × 10²³
A mole is a counting unit, like a dozen, except it is 6.022 × 10²³ particles. The molar mass is the mass of one mole, and you read it straight off the periodic table. 8.00 g of CO₂ is 0.182 mol, which is about 1.1 × 10²³ molecules.
The ideal gas law
pV = nRT p in Pa, V in m³, n in mol, R = 8.314 J/(mol·K), T in kelvin (°C + 273.15)
Rearranged as V = nRT/p, it tells you how much room a gas needs at a given pressure and temperature. For a fixed amount of gas in a fixed volume, p/T stays constant, so warming a sealed container raises its pressure.
States of matter inside the cartridge
In the liquid, the molecules are close together and slide past each other. When the seal opens, the pressure falls below the vapour pressure and molecules escape from the liquid very quickly. That is boiling. Boiling takes energy from the surroundings, so the cartridge gets very cold, and water vapour from the air freezes onto it. That is the frost.
!
Why cool storage matters. The vapour pressure of liquid CO₂ climbs steeply with temperature. About 57 bar at 20 °C, 64 bar at 25 °C, 72 bar at 30 °C, and above 31.1 °C (the critical temperature) it is not a liquid at all. A cartridge left in the sun launches differently from one kept in the shade. Consistent cartridges mean consistent races.
04Gas expansion model
Set the mass of CO₂ and the room conditions to see how much gas leaves the cartridge. The second chart shows the vapour pressure of liquid CO₂ inside a sealed cartridge as it warms up. That curve is the reason for the shade rule.
The ideal gas law is used for the expanded gas. The vapour-pressure curve uses published CO₂ data from 0 to 31 °C. Above 31.1 °C the CO₂ is supercritical, so the curve stops.
—molMoles, n = m/M
—Molecules
—LVolume of gas
—×Bigger than the liquid
05Worked example
Moles in the cartridge. m = 8.00 g, M(CO₂) = 12.01 + 2(16.00) = 44.01 g/mol.
n = m / M = 8.00 / 44.01 = 0.1818 mol
N = n × NA = 0.1818 × 6.022 × 10²³ = 1.09 × 10²³ molecules
Volume after expansion at 25 °C (298.15 K) and 101 325 Pa:
V = nRT / p = 0.1818 × 8.314 × 298.15 / 101 325
V = 4.45 × 10⁻³ m³ = 4.45 L
Sense check: liquid CO₂ has a density of about 0.77 g/cm³, so 8 g of liquid is about 10 cm³. The gas is around 430 times bigger. That expansion, forced through a small nozzle in a third of a second, is the thrust in LAB-05.
06Student questions Teacher mode is off. Answers are hidden.
Q1 · Moles[2]
A bigger 12.0 g cartridge is used in another class. How many moles of CO₂ does it hold? How many molecules?
Answer key
n = 12.0 / 44.01 = 0.273 mol
N = 0.273 × 6.022 × 10²³ = 1.64 × 10²³ molecules
Q2 · Gas law[3]
Find the volume of 0.182 mol of CO₂ at 20 °C and 101 325 Pa. Show the conversion to kelvin.
Answer key
T = 20 + 273.15 = 293.15 K
V = nRT/p = 0.182 × 8.314 × 293.15 / 101 325
V = 4.38 × 10⁻³ m³ = 4.38 L
Q3 · Explain[3]
A fired cartridge comes back covered in frost, even on a hot day. Explain why in terms of particles.
Answer key
When the seal opens the pressure drops, so the liquid CO₂ boils very quickly (1). Boiling needs energy (latent heat), which is taken from the metal cartridge and the remaining liquid, so the cartridge cools far below 0 °C (1). Water vapour in the air then condenses and freezes on the cold surface. The frost is water, not CO₂ (1).
Q4 · Apply[3]
A sealed cartridge is at 57 bar at 20 °C. Estimate the pressure at 35 °C using p/T = constant for the gas. Then explain why the real value is higher, and why teams keep cartridges cool.
Answer key
p₂ = p₁ × T₂/T₁ = 57 × 308.15/293.15 = 59.9 bar
The real value is higher (around 80 bar, and it is no longer a liquid because 35 °C is above the critical temperature of 31.1 °C). The cartridge holds a liquid whose vapour pressure rises steeply with temperature, not an ideal gas (1). A different pressure means a different thrust and inconsistent launches, so cartridges are kept at a steady, cool temperature (1).
07Printable worksheet The answer key prints as well when teacher mode is on
Team Nightmare · STEM Subject Lab
NM-LAB-06 · The CO₂ Cartridge: Moles, Gas & Pressure
Name ______________________ Class __________ Date __________
Chemistry 40 minutes Links to LAB-05
Formula bank
n = m / M N = n × 6.022×10²³
pV = nRT R = 8.314 J/(mol·K)
T(K) = T(°C) + 273.15
Data
Ar: C = 12.01, O = 16.00. Cartridge: 8.00 g of CO₂. Liquid CO₂ density about 0.77 g/cm³. Critical temperature 31.1 °C.
3. [3] T = 300.15 KV = 0.182 × 8.314 × 300.15 / 100 000 = 4.54 × 10⁻³ m³= 4.54 L One mark for kelvin, one for the substitution, one for the answer in both units.
5. [3] The pressure inside falls when the seal opens (1). The liquid is now above its boiling point at that pressure, so molecules escape from it very quickly. It boils (1). Boiling takes energy from the surroundings, so the cartridge cools, and the gas molecules, far apart and fast, rush out through the nozzle (1).
6. [2] The vapour pressure of liquid CO₂ rises steeply with temperature (1). A warmer cartridge launches with a different, higher and less predictable pressure, so the runs are inconsistent. Cool storage keeps every launch the same (1).