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# Amount of Substances

## Key Facts & Summary of Amount of Substances

• Molar Mass is the mass in grams of 1 mole of a substance and is given the unit of g mol-1
• The mole is the amount of substance in grams that has the same number of particles as there are atoms in 12 grams of carbon-12.
• One mole of a defined entity contains 6.02 x 1023 of that entity
• Molarity, M, indicates the number of moles of a solute in 1 L of a solution
• Molality, m,indicates the number of moles of solute dissolved in exactly one kilogram of solvent.

The amounts of the substances are measured in units of mass (g or kg), volume (L) and mole (mol). Unit interconversions are based on the definitions of the units, and converting amounts from g or kg into mol is based on atomic masses of the elements.

Atomic mass is defined as the mass of one mole of element.

A mole of any element is the amount of the element that contains a defined number of atoms, called Avogadro's number ( 6.02 x 1023 ). So a mole of sodium is the amount of sodium which contains 6.02x10 23 atoms of the element.

Some other examples are:

1 mole of  copper atoms will contain 6.02 x 1023 atoms

1 mole of carbon dioxide molecules will contain 6.02 x 1023 molecules

1 mole of sodium ions will contain 6.02 x 1023 ions

## Molecules

Molecules  are the natural units of substances. Molecules are groups of atoms bonded together,  except monatomic molecules of inert gases He (helium), Ne (neon), Ar (argon), Kr (kripton), Xe (xenon), and Rn (radon).

For example, molecules of oxygen, water, and phosphorous are O2 , H2O , and P4 respectively.

Fig. 1 graphic rapresentation of molecules. From left to right: oxygen, water and phosphorus.

Different substances have different molecular masses. Equal numbers of moles of different substances have different masses, but equal masses have different numbers of atoms, molecules, or moles. This can sound a little bit complicated, but it will all make sense eventually.

The stoichiometric relationships between reactants and products in a reaction is far more simpler if we deal with it using moles instead of grams.

As said above, moles (mol) represent amounts of substances in the unit of Avogadro's number (6.02 x 1023) of atoms and molecules. Therefore a mole of Fe2+ has 6.02 x 1023ions, and a mole of Fe2O3 has 1.204x1024  Fe and 1.8066x1024 O atoms, so a total of 3.0x1024  Fe and O atoms.

## Molar Mass

It is also very important to convert masses in grams or mol. The number of moles of a substance in a sample is the mass in g divided by the molar mass,

Here the formula:

mole = mass(g) * molarmass(g/mol)

. Since density is the mass divided by its volume,

density=mass(g)volume(cm3)

mass=density(gcm−3)×volume(cm3)

Let's use some examples of chemical reactions to see how important and easier is to use moles instead of grams.

Suppose we combine 1 g of calcium oxide (CaO) with 1 g of water (H2O). The product we get is Ca(OH)2. Here's the equation:

CaO(s)+H2O(l)→Ca(OH)2(solaq)

This chemical reaction is balanced and every molecule of water reacts with one CaO formula unit (here we cannot use the term molecule because it's an ionic solid, and each Ca+2  ion is surrounded with oxide ions).

The question is: how much calcium hydroxide is produced by this reaction?

Once all of one reactant has been used, whatever is left of the other will stop reacting, because of the law of definite proportions: we won't change the ratio of O:H:Ca in the product. So will we get solid calcium hydroxide with calcium oxide left over, or will we have water left over, and thus get Ca(OH)2(aq)?

To answer this question, we can convert both masses (1 g of each) to the number of molecules or formula weights, but, as you can imagine, this would be inconvenient because the number would be very big and difficult to do calculation with!

Instead, we use moles. This is a convenient quantity because it converts amu (atomic mass units) to grams. The atomic weight of carbon is (on average) 12.011 amu/atom. It is also 12.011g/mol. In other words, 1g = 6.02 x 1023 amu. Usually, a mol of a substance is a useful, practical amount, somewhere between a few grams and a few kg.

## Solutions

A solution is a mixture formed when a solute dissolves in a solvent. The most common solvent used in chemistry is water, although it is not the only one. The solute can be a solid, liquid or a gas. Molar concentration can be measured for solutions as well.

The molarity of a solution indicates the number of moles of a solute in 1 L of a solution. (Important to note is that molarity is spelled with an "r" and is represented by a capital M.)

### Calculate Molarity of a Solute

To calculate the molarity of a solute in a solution we need to know:

• The moles of solute present in the solution.
• The volume of solution (in liters) containing the solute.

To calculate molarity we use the equation:

molarity = moles of solute / volume of solution in litres

The volume is measure is dm3. The unit of molar concentration is mol dm-3 ;

it can also be called molar using symbol M

Molality, m,indicates the number of moles of solute dissolved in exactly one kilogram of solvent. (Note that molality is spelled with two "l" s and represented by a lower case m.)

To calculate the molality of a solute in a solution we need to know”

• The moles of solute present in the solution.
• The mass of solvent (in kilograms) in the solution.

To calculate molality we use the equation:

molality = moles of solute / mass of solvent in kg

### Making Dilutions

A solution can be made less concentrated by dilution with solvent. If a solution is diluted from the initial volume V1 to the final volume V2, the molarity of that solution changes according to the equation:

M1 V1 = M2 V2

Where M1 usually refers to as the initial molarity of the solution V1

and

M2 refers to the final concentration of the solution  V2

The volume units must be the same for both volumes in this equation.

Remember: the number of moles of solute does not change when more solvent is added to the solution. Concentration is what changes during dilutions.