In which state of matter, solid, liquid or gas, are the particles (i) moving around fastest, (ii) farthest apart? (iii) What term is used to describe the spreading out, as shown in the photograph, of the smoke spewed out by an erupting volcano? The combined gas law states that $$\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$$ constant for a fixed mass of gas - Leaving Cert Chemistry - Question b - 2020

In a gas, the particles are farthest apart compared to solid and liquid states.

The term used to describe the spreading out, as shown in the photograph, is diffusion.

Using the combined gas law, we have:

$\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$

Substituting the known values:

• $p_1 = 2 \times 10^3 \text{ Pa}$,
• $V_1 = 120 \text{ cm}^3$,
• $T_1 = 819 \text{ K}$,
• $p_2 = 1 \times 10^5 \text{ Pa}$,
• $T_2 = 273 \text{ K}$,

We need to find $V_2$:

$\frac{2 \times 10^3 \cdot 120}{819} = \frac{1 \times 10^5 \cdot V_2}{273}$

This simplifies to:

$V_2 = \frac{(2 \times 10^3 \cdot 120 \cdot 273)}{(819 \cdot 1 \times 10^5)}$

Calculating gives: $V_2 = 80.0 \text{ cm}^3$

One of the laws is Boyle's Law, which states that pressure and volume are inversely proportional at constant temperature: $P \propto \frac{1}{V} \quad or \quad PV = k$