Amounts of Chemicals

Amounts of Chemicals:

Atoms and molecules are so small that we cannot directly measure the number in a sample or the number that change in a reaction. Instead, we use measurements such as the mass or volume to measure the amount. The volume can be converted to a mass using the density. The number of atoms or molecules present is related to the mass or volume through the atomic or molecular mass respectively. The molecular mass is determined by multiplying the atomic mass of each atom in a compound by the number of times the symbol appears in the formula of the compound.

For both cooks and chemists, it is most convenient to measure mass in grams and volume in litres (or millilitres).

A cook buying a large number of eggs will ask for them by the dozen, because it is less fiddly than dealing with the number of individual eggs. The chemist has the same problem with molecules, except that the number of molecules we deal with is huge. We count atoms and molecules not by the dozen but by the mole. For the cook,

• 1 dozen eggs corresponds to 12 eggs.
• 2 dozen eggs corresponds to 24 eggs.
• 3 dozen eggplants corresponds to 36 eggplants.
• 2 dozen hydrogen atoms corresponds to 24 hydrogen atoms.

For the chemist,

• 1 mole of hydrogen atoms corresponds to 6.022 × 10²³ hydrogen atom.
• 2 moles of water molecules corresponds to 2 × 6.022 × 10²³ water molecules.
• 2 moles of eggs corresponds to 2 × 6.022 × 10²³ eggs.

The principle is the same: a dozen always means 12 of a thing and a mole always means 6.022 × 10²³ of a thing. The only difference is the scale.

The molar mass is the mass, in grams, of one mole of a substance. The unit for the mole is “mol”, just like the unit for the dozen is “doz”.

Molar mass is referred to as: atomic mass if the substance is an element, molecular mass if the substance is a molecule and formula mass if the substance is an ionic compound.

Converting between mass, moles and molar mass

Converting between mass, moles and molar mass:

When performing any calculations in science, an appreciation of the accuracy and significance of the measurements is vital - just ask an athlete under suspicion of taking performance enhancing drugs. If you are unfamilar with the proper way to handle signficant figures, read the iChem online tutorial (identical to the E9 week 4 pre-laboratory information)

Dealing with moles is very important and you will do so many times. There are three possible scenarios:

You know the mass and the molar mass and want to work out the number of moles

You know the mass and the molar mass and want to work out the number of moles:

number of moles (in mol) =	mass (in g)	or	n =	m
	molar mass (g mol-1)			M

You know the number of moles and the molar mass and want to work out the mass

You know the number of moles and the molar mass and want to work out the mass:

mass (in g) =

number of moles (in mol) × molar mass (in g mol-1)

You know the number of moles and the mass and want to work out the molar mass

You know the number of moles and the mass and want to work out the molar mass:

molar mass (in g mol-1) =	mass (in g)	or	M =	m
	number of moles (in mol)			n

Remembering these relationships

Remembering these relationships:

Use a finger to cover up the quantity you want to calculate. The other two values show you how to do the calculation. To calculate the number of moles, cover up n and you are left with m / M. Hence, n = m / M To calculate the mass, cover up m and you are left with n M. Hence, m = n × M To calculate the molar mass, cover up M and you are left with m / n. Hence, M = m / n

Examples

Work through these examples carefully to see how the rules are applied and then test yourself with the self test quiz.

1. What is the mass of 2 moles of glucose (C₆H₁₂O₆)?

1. 2.0 mol of glucose (C₆H₁₂O₆) has a mass of 360 g:

The molar mass of C₆H₁₂O₆ is:

molar mass = 6 × 12.01 (C) + 12 × 1.008 (H) + 6 × 16.00 (O) = 180.158 g mol^-1. (You can use the molar mass calculator to do this when you are happy with the method needed).

Using m = n × M,

m = (2.0 mol) × (180.156 g mol^-1) = 360 g

2. How many moles are present in 45.0 g of NaOH(s)?

2. 45.0 g of NaOH(s) contains 1.13 mol:

The molar mass of NaOH is:

molar mass = 22.99 (Na) + 16.00 (O) + 1.008 (H) = 39.998 g mol^-1. (You can use the molar mass calculator to do this when you are happy with the method needed).

Using n =	m	,   n = =	45.0 g	= 1.13 mol
	M		39.998 g mol-1

3. What is the molar mass of protein X if 1200 g contain 0.123 mol?

3. If 1200 g of a protein corresponds to 0.123 mol, its molar mass is 9800 g mol^-1:

Using M =	m	,   M = =	1200 g	= 9800 g mol-1
	n		0.123 mol

Self test quizzes

Test your understanding using the quizzes below.