# Stoichiometry

Compounds are substances composed of two or more elements in a fixed composition. Molecular weight is the mass (in amu) of the constituent atoms in a compound as indicated by the molecular formula. Molecular weight is numerically equal to molecular mass (amu)

1 amu = 1 g/mol

Carbon has 12 amu and weighs 12 g/mol. The molecular structure shows the arrangement of the atoms of a molecule while the molecular formula indicates how much of a particular atom is in the molecule. Commonly used metric units are Molarity, molality and molar mass. Molar mass is the mass of one mole (Avogadro’s number or 6.022 × 1023 particles) of a compound and is usually measured in grams per mol.

Molarity (M) = mol/L

Molality (m) = mol/kg

molar mass = g/mol.

To calculate percent composition by mass, determine the mass of the individual element and divide by the molar mass of the compound. 1 mole is the same as 1 mol and it equals to 1 Avogadro’s number (6.022 × 1023 particles). The density of an object is given as:

Density = mass / volume (kg/m3)

Often times, specific gravity is used and it is given by the formula:

specific gravity = density of substance / density of water

density of water = 1 g/mL (or 1 g/cm3)

specific gravity of water = (1 g/cm3) / (1 g/cm3) = 1

Common oxidizing agents include oxygen, ozone, permanganates, chromates, dichromates, peroxides, lewis acids and oxygen containing compounds. Common reducing agents includes hydrogen, metals, Zn/HCl, Sn/HCl, lithium aluminium hydride, sodium borohydride, lewis bases and hydrogen containing compounds. An element in a single oxidation state reacts to form 2 different oxidation states. Disproportionation can occur when a species undergo both oxidation and reduction. For example:

2Cu+ → Cu + Cu2+

Here, the Cu+ acts as both oxidizing and reducing agent and simultaneously reduce and oxidize itself. The oxidized Cu+ becomes Cu2+ and the reduced Cu+ becomes Cu. To write a chemical equation, certain conventions must be used:

Phases refer to whether the substance is a solid (s), liquid (l), gas (g) or aqueous (dissolved in water) (aq). An equation with coefficients is a balanced equation. It shows that the number of each atoms on one side of the equation is the same as the number of atoms on the other side. In regard to direction, a single head arrow denotes the reaction goes to completion in the direction of the arrow. A double-sided arrow denotes a reaction in equilibrium and a double-sided arrow with one side larger than the other denotes an equilibrium in favor of the side of the larger arrow. The superscripted charge denotes charge and magnitude of compound. Neutral charges are not denoted.

In balancing an oxidation-reduction (redox) equation, you first separate the equation into half reactions. There will be 2 half equations: one will be oxidation, the other reduction. Half equations contain only species of interest, those containing the atom that undergoes a change in oxidation state. Anything that is not covalently attached to the atom is not part of the species of interest and anything that does not undergo a change in oxidation state is a spectator ion/species. After separating the redox reaction, balance each of the half reactions. Both charge and atoms must be balanced. Under acidic conditions add H2O to the side that needs the oxygen atom, then add H+ to the other side. Under basic conditions, add 2OH to the side that needs the oxygen atom, then add H2O to the other side. You can either balance out the atoms first, then charge or you can treat the species of interest as a single atom (those that undergo a change in oxidation number) and then balance it. The half reactions are then recombined. Multiply each half reaction by a factor, such that when you add them together, the electrons cancel out. Combine any identical species on the same side of the equation and cancel out any identical species on opposite sides of the equation. Add back in the spectator ions. If you had treated the species of interest as a single atom, now is also the time to balance out the oxygens and hydrogens. Check to make sure that both sides of the equation have equal number of atoms and neutral net charge.

In chemical reactions one reactant may be used up before the others. The reaction stops as soon as any reactant is totally consumed, leaving the excess reactants as leftovers. The reactant that is completely consumed in a reaction is called the limiting reactant because it determines, or limits, the amount of product formed. Balanced equations can be used to determine the limiting reagent, which is the reactant that will be consumed first in a chemical reaction. The other reactants present are termed excess reagents. In calculating the theoretical yield, first find out what your limiting reactant is. Then, use your limiting reactant as the stoichiometric basis to calculate how much product you will get. During an actual process, the experimental yield is always less than the theoretical yield because of loss during steps of the reaction or even preparation. You can also have a higher experimental yield if more reactants were added in the beginning than initially thought. Percent yield is calculated by dividing actual yield by theoretical yield and converting to a percentage.

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