# Atoms And Molecules

## Avogadro's constant

**6.02x10 ^{23}**. This is the number of molecules in 12g of carbon 12. It is also the number of molecules in exactly one mole of atoms.

## Mole

This is the standard unit of measurement for "amount of substance." One mole of a substance contains 6.02 x 10^{23} molecules.

## Molar mass:

The weight of one mole of an element. This can be found above an element symbol on the periodic table.

## Conversion between molecules, mass, and moles

- Convert from the number of molecules to moles by dividing by 6.02x10
^{23} - Convert from moles to grams by multiplying by the molar mass

## Kinetic theory of matter

The **kinetic** molecular **theory of matter** states that: matter is made up of particles that are continually moving. All particles have energy, but the energy varies depending on the temperature of the matter.

**Brownian motion is t**he constant erratic movement of small particles suspended in a liquid or gas when viewed under a microscope. This is caused by the constant bombardment from the molecules in the medium. This provides evidence for the kinetic theory of matter.

# Thermal Concepts

## Internal energy

Internal Energy is the sum of all random kinetic energies and mutual potential energies of the particles of the body or system. It is measured in joules (J).

${E}_{t}={E}_{k}+{E}_{p}$

**Average Kinetic energy: **The average amount of energy stored in each particle due to its motion. The faster it vibrates or moves, the more kinetic energy

**Potential Energy: **The energy required to stretch the intermolecular bonds.

## Temperature

This is a measure of how hot or cold a substance is. More specifically, it is a measure of the random average kinetic energy. It is measured in °C or K.

$K=C+273$

The average kinetic energy of a molecule is given by this equation (in data booklet):

${E}_{k}=\frac{3}{2}kt$

- k is the Boltzmann constant
- T is the temperature in Kelvin

# Heat

Heat is the transfer of energy from a high temperature to a low temperature. The transfer occurs until both objects are at **Thermal equilibrium**

## Heat transfer

**Conduction:** When the molecules at one end of a solid object are given energy, they vibrate more. This disturbs the neighboring molecules and passing the energy along.

**Convection:** The transfer of heat energy via liquid or gas. When heated fluid expands, marking it less dense, causing it to rise in the surrounding denser cooler fluid.

**Radiation is the** direct transfer from one body to another via infrared radiation. Bodies of darker color both radiate and absorb the best.

## Thermal capacity

The heat required to raise the temperature of a body by 1k.

Formula: $Q=c\u2206T$

Unlike specific heat capacity, this does not require mass.

## Specific heat capacity

**Specific heat ****capacity:** Amount of energy (joules) required to raise 1kg of a substance by one degree (Kelvin or Celcius). Measured in **J/kg°K**

Formula: $$c=Q/{mΔT}$$

The change in thermal energy is equal to mass times specific heat capacity times by change in temperature.

### Example question and answer

*Jacob has 1500g ^{ } of water, which is at 17°C. How much heat must he add in joules, for the water to begin to boil? The specific heat capacity of water is 4.2 KJ/kg°C. *

- First, pull out the values needed from the question:
- Change temperature = 100-17= 83°C
- Mass = 1500g = 1.5kg
- SHC = 4.2 KJ/g°C.= 4200j

- Then put into the formula:
- $Q=4.2\times 1.5\times 83=522.9kj$

## Specific latent heat

**Specific Latent Heat: **Energy required to change the state of 1 kg of a substance. The unit is ** j/kg**

When you change the state of a substance, the energy stops being used to change the temperature but instead to break the bonds. Because of this, during a period of state change, the temperature will remain constant.

The amount of energy required to change the state of a substance is called the** latent heat**. Latent is a word which means that something exists yet is hidden, so this is the "hidden temperature" change.

### Fusion and vaporization

Since there are two state changes, there are also two types of specific latent heat

**Latent heat of fusion: **Energy (kJ) to change a solid into a liquid

**Latent heat of vaporization: **Energy (kJ) to turn a fluid into a gas.

### Calculating Latent heat changes

The energy to change the state is equal to mass times specific latent heat for that state.

# Modeling An Ideal Gas

## Assumptions of an ideal gas

- The volume of atoms is much smaller than the volume of gas
- Atoms are perfectly elastic spheres. (they don't lose energy in collisions)
- There are no intermolecular forces between the gas molecules.
- There is no potential energy as this requires inter-molecular forces
- The collisions all have uniform velocity

- High temperatures and low pressures

**The IB will usually only ask for three assumptions, so if you remember these you have a very high chance of getting full points on any relevant question.**

## Ideal gas law

$pV=nrT$

- P-pressure (pa)
- v-volume (${m}^{3}$)
- n-moles
- r - gas constant (8.31)
- t - temperature (kelvin

## Boyles law

- The pressure of a fixed mass of gas at constant temperature is inversely proportional to its volume
- The pressure of a fixed mass of gas at constant volume is proportional to its temperature
- The volume of a fixed mass of gas at constant pressure is proportional to its temperature.

## Types of processes

- Isobaric -constant pressure
- Isovolumetric - constant volume
- Isothermal - constant temperature
- Isolated - constant mass

**Thermodynamic ****cycle****:** A set of operations which ultimately return to its original state

## The Mother of all Physics Questions

This really is the hardest multi-choice question on this topic.

#### A: C (W=f*d and f = A * P therefore W = P * change in V )

# Editors

- joeClinton - 890 words.
- CD_FER - 132 words.

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