Pressure, Amount of Substance, and the Ideal Gas Law
Pressure: Force Distributed Over Area
Pressure
Pressure is the force applied per unit area.
Mathematically, it is expressed as:
$$
P = \frac{F}{A}
$$
where:
- $P$ is the pressure (in pascals, Pa)
- $F$ is the force applied (in newtons, N)
- $A$ is the area over which the force is distributed (in square meters, m²)
Pressure is a scalar quantity.
HintThe unit of pressure, the pascal (Pa), is equivalent to one newton per square meter ($\text{N m}^{-2}$).
ExampleConsider a block weighing 100 N resting on a surface with an area of 0.5 m². To find the pressure it exerts:
$$P = \frac{F}{A} $$
$$=\frac{100 \, \text{N}}{0.5 \, \text{m}^2} = 200 \, \text{Pa}$$
ExampleA cylinder with a weight of 500 N and a base area of 0.2 m² exerts a pressure of:
$$
P = \frac{500 \, \text{N}}{0.2 \, \text{m}^2} = 2500 \, \text{Pa}
$$
Always ensure the force is perpendicular to the surface when calculating pressure.
Amount of Substance: The Mole and Avogadro’s Constant
The amount of substance is measured in moles, a fundamental concept in chemistry and physics.
Mole
A mole is defined as the amount of substance containing as many particles (atoms, molecules, etc.) as there are atoms in 12 grams of carbon-12.
This number is the Avogadro constant,$N_A$, approximately $6.022 \times 10^{23}$ particles per mole.
Calculating Moles
If a substance contains $N$ particles, the number of moles $n$ is given by:
$$
n = \frac{N}{N_A}
$$
where:
- $n$ is the number of moles
- $N$ is the total number of particles
- $N_A$ is the Avogadro constant ($6.022 \times 10^{23}$ particles/mol)
- The molar mass of a substance (in grams per mole) tells you the mass of one mole of that substance.
- For example, water (H₂O) has a molar mass of $18 \text{.g mol}^{-1}$l.
How many moles are in $1.2 \times 10^{24}$ molecules of water?
Solution
Using the formula:
$$n = \frac{N}{N_A} $$
$$= \frac{1.2 \times 10^{24}}{6.022 \times 10^{23}} $$
$$\approx 2 \, \text{mol}$$
The Ideal Gas Law: A Universal Equation
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas which relates the pressure, volume, temperature, and amount of substance in a gas.
It is expressed as:
$$
PV = nRT
$$
where:
- $P$ is the pressure (in pascals, Pa)
- $V$ is the volume (in cubic meters, m³)
- $n$ is the number of moles
