Moles and molar masses

Avogadro constant $N_A$

  • Avogadro constant specifies the ammount of particles in a mole of any substance

$$1\ N_A=6.022\cdot{10^{23}}\ mol^{-1}$$

  • it is defined as the number of atoms in precisely 12 grams of $^{12}C$ isotope

Mole of a substance $mol$

  • a mole is precisely the Avogadro contant number of particles
  • with the weight of an atom, the wieght of a mole increases
  • the number of moles of a substance is called ammount of substance $n$

Molar mass $M$

  • molar mass is the weight of one mole of a substance
  • molar mass of an atom is derived from the relative atomic weight (which can be found in the periodic table)
    • relative atomic weight $m_a$ has specifies the weight of a mole of a substance composed only of single atoms
    • molar mass specifies the weight of a mole of a substance composed of either single atoms or molecules
  • molar mass of a molecule is the sum of relative atomic weights of its individual atoms

$$M=\sum{m_a}$$

Relationships

  • calculating the mass of a substance

$$m=n\cdot{M}$$

  • thus:

$$n=\cfrac{m}{M}\ \ \ M=\cfrac{m}{n}$$

  • calculating the number of particles $N$ of a substance

$$N=n\cdot{N_A}$$

  • thus:

$$n=\cfrac{N}{N_A}\ \ \ N_A=\cfrac{N}{n}$$

Elemental composition of pure substances

Denoting elements

  • writing down the composition of paticles combines using letters (the symbols of elements) and numbers
  • numbers are written in four indexes around the symbol of the element
    • top right index denotes the overall charge of the prticle
    • bottom right index denotes the number of atoms constituting the particle
    • bottom left index denotes the number of protons
    • to left index denotes the overall number of nucleons
      • it is also reffered to as the mass number
  • ex. $_8^{18}O_2^{-1}$ - dioxygen-18 (-1) anion

Denoting pure substances

Structural formula

  • structural formulae denote every atom and bond of the substance
    • some formulae also add free electron pairs
  • ex.
Structural formula of hydrogen peroxide
Structural formula of hydrogen peroxide
  • the structural formula is sometimes condensed
    • groups of distinct physical or chemical properties are written together
  • ex. Condensed strucural formula of hydrogen peroxide $$HO-OH$$
  • it is most commonly used in organic chemistry

Molecular formula

  • molecular formulae denote only the numbers of atoms in the substance
  • ex. Molecular formula of hydrogen peroxide $$H_2O_2$$
  • it is most commonly used in inorganic chemistry

Empirical formula

  • empirical formulae denote only the most simplified ratios of individual atoms compared to one another
  • it is based on simple observations of an unknown substance (hence the name) that determine which atoms can be found in a substance
  • it also obeys the law od definite proportions

The simple ratio of atoms in any sample of a pure substance is always preserved.

  • ex. Empirical formula of hydrogen peroxide $$HO$$
  • it omits all structural descriptors and thus can lead to confusion and misrepresentation

Mass fraction $w$

  • mass fraction tells us the fraction of mass a component of a substance takes up

$$w_i=\cfrac{m_i}{m}$$

  • where:
    • $w_i$ is the mass fraction of substance $i$
    • $m_i$ is the actual mass of substance $i$
    • $m$ is the actual mass of the whole sample