Carbon dioxide is stored under pressure in liquid form in a fire extinguisher - Leaving Cert Chemistry - Question b)(ii) - 2007

To find the volume of carbon dioxide, we can use the Ideal Gas Law, represented by the formula: $PV = nRT$

Where:

• $P$ = pressure (1.01 × 10² Pa)
• $V$ = volume (unknown)
• $n$ = number of moles
• $R$ = ideal gas constant (approximately 8.314 J/(mol·K))
• $T$ = temperature (290 K)

First, we calculate the number of moles, $n$: $n = \frac{mass}{molar\ mass} = \frac{2000\ g}{44.01\ g/mol} = 45.4\ moles$

Now, substitute $n$ into the Ideal Gas Law: $V = \frac{nRT}{P} = \frac{(45.4\ mol)(8.314\ J/(mol·K))(290\ K)}{1.01 × 10²\ Pa}$

After calculating, we find: $V \approx 1.069 - 1.10\ m^3$

For helium gas, we first calculate the number of moles required to fill the same volume: Using the Ideal Gas Law again, we have:

$n_{He} = \frac{PV}{RT}$

Substituting the known values: $n_{He} = \frac{(1.01 × 10^2\ Pa)(1.069\ m^3)}{(8.314\ J/(mol·K))(290\ K)}$

Calculating this gives us roughly: $n_{He} \approx 22.4\ moles$

Now, the mass of helium is: $mass_{He} = n_{He} \times molar mass_{He} = 22.4\ moles \times 4.00\ g/mol = 89.6\ g \approx 0.090 kg$

Carbon dioxide has stronger intermolecular forces (London dispersion, Van der Waals, dipole-dipole) compared to helium. These forces arise from its larger molecular mass and greater polarizability, making it more easily liquefied.