Atoms are too small for scientists to count individually- 500,000 carbon atoms stacked together equal the width of a single strand of human hair!
- In this article about the amount of substance, you will learn about Avogadro’s constant (L) and how to calculate the number of moles (n).
- You will also discover relative atomic mass (Ar) and why we use the unified atomic mass unit (u).
- We will discuss Percentage Yield and why actual yield is lower than theoretical yield. Finally, you will learn the ideal gas equation and kinetic gas theory.
- This is a summary article; to learn more, tap on the linked topics.
What is the amount of substance?
The amount of substance (n) means the number of particles or elementary entities in a sample. It is also called the chemical amount.
The unit for the amount of substance is the mole.
An elementary entity is the smallest amount of a substance that can exist. Elementary entities can be atoms, molecules, ions, or electrons.
When talking about amounts of substance you must specify what elementary entity is involved. For example, consider the element oxygen.
You might assume the elementary entity for an amount of oxygen is the oxygen atom- O. However, at standard temperature and pressure two oxygen atoms combine into molecular oxygen- \(O_2\) . This means oxygen’s elementary entity is \(O_2\) .
When we talk about the amount of substance of covalent compounds, we mean their molecular formula. For ionic compounds, we mean their formula units.
Fig. 1 - Oxygen is a diatomic particle. It exists in pairs so the elementary entity for oxygen is O2
What is the mole?
A chemical mole is another way of saying an exact quantity. Just like we say 'a dozen' to mean 'twelve things', a mole is '602 hexillion things'. That's 602,200,000,000,000,000,000,000! We write it as 
for short.
Fig. 2 - A mole is 602 hexillion things!
The number 
is also known as Avogadro's constant (L). It is named after an Italian scientist called Amedeo Avogadro. He discovered that equal volumes of gases contain the same number of molecules when under the same conditions. Scientists used this discovery to calculate Avogadro's constant.
Avogadro's constant (L) is the exact number of atoms in 12 grams of carbon-12. This number is 
. We give it the units \(mol^-1\) , which you read as 'per mole'.
The mole is the SI unit for the amount of substance.
You can find the number of moles using this formula:
\(n\space\)= \(\frac {m} {M}\)
or
\(\text{number of moles}\space\) = \(\frac { \text {mass in grams} } {\text {Molar mass}}\) n: number of moles
m: mass in grams
M: molar mass (the mass of 1 mole in grams)
The amount of elementary entities in a mole is equal to the number of atoms in 12g of the carbon-12 isotope.
This means that in 1 mole of any substance, there are exactly 
elementary entities or Avogadro's constant.
1 mole of a substance weighs 80 g and you have 10 g of it. How many moles of the substance do you have?
\(n\space\)= \(\frac {m} {M}\)
\(n\space\)= \(\frac {10} {80} \)
\(n= 0.125 mol\)
Why is the mole important?
The mole is essential when we talk about chemical reactions. Have a look at this equation:
$$2H_2O+O_2\rightarrow 2H_2O$$
We can say "oxygen and hydrogen react to make water"
or
"two molecules of hydrogen and one molecule of oxygen react to make water".
Did you notice that we need two times as many molecules of hydrogen as we need oxygen? So if we had 1 mole of hydrogen and 1 mole of oxygen they would have the same number of molecules - Avogadro's constant. To make sure we have twice as many hydrogen molecules, we need twice as many moles of hydrogen.
That means we can also say "2 moles of hydrogen react with 1 mole of oxygen to make 2 moles of water".
The mole is helpful because it allows you to read chemical equations by the number of moles of each substance. You can then figure out the exact amounts of substances that are reacting.
The mass of one mole of a substance is equal to its formula mass.
What is relative mass?
Scientists measure the mass of an atom by comparing it to \(\frac {1} {2} \) the mass of a neutral carbon-12 atom. We call this relative mass.
We express relative mass by referring to the unified atomic mass unit (u or Dalton).
One dalton (1u) equals \(\frac {1} {2} \) the mass of a stable atom of carbon-12 or \(1.660539040(20) \times 10^{27}\space kg\)
We compare all atoms to \(\frac {1} {12} \) of carbon-12 because it equals 1u.
u is the unit of measurement for atomic mass. 1u equals \(\frac {1} {12} \) the mass of a carbon-12 atom.
Why do we use relative masses?
We use relative masses because atoms are so tiny that using their actual weights makes calculations tricky. Instead of using the actual mass of atoms in problems, scientists compare all atoms to a standard atom: carbon-12. They use carbon-12 because it is a stable isotope and they can measure its mass accurately. Carbon-12 is the isotope of carbon with 6 protons and 6 neutrons. They found out the carbon-12 atom weighs \(6\times 10^{-23}\space grams\) .
Fig. 3 - Carbon-12 Olive
Scientists gave carbon-12 a mass of 12u because they found it easier to say "carbon-12 weighs 12u". By comparing the weight of all other atoms to carbon-12 they discovered the hydrogen atom weighs \(\frac {1} {12} \) of the carbon-12 atom. So they gave hydrogen a relative mass of 1u.
hydrogen = carbon mass ÷ 12
=12u ÷ 12
=1u
What is relative atomic mass?
The atomic mass of an element will vary from one isotope to another. The figure we see for an element's atomic mass on the periodic table is the relative atomic mass.
Relative atomic mass \(A_r\) is the average mass of all the isotopes of an element, weighed by the abundance of each isotope on Earth.
You can calculate the relative atomic mass using this formula:
\(A_r\) = \(\frac {\text {isotope mass x isotope abundance} } {\text {100} } \)
What is relative molecular mass?
The weighted average of the mass of a molecule compared to \(\frac {1} {12} \) of the mass of a carbon-12 atom is called the relative molecular mass (
or RMM).
What is percentage yield?
When we compare the actual amount of product we get from a chemical reaction to the amount we theoretically could have got, it is called Percentage Yield.
Percentage yield measures the effectiveness of a chemical reaction. It tells us how much of our reactants (in percentage terms) successfully turned into a product.
We calculate it like this:
\(percentage\space yield\)= \(\frac {actual\space yield} {theoritical\space yield}\times100 \)
Christina calculated the theoretical yield of an experiment to be 16.5g of sodium chloride. As a result of the reaction the got 12.8g of sodium chloride. Calculate the percentage yield of Christina's experiment.
actual yield / theoretical yield x 100
(12.8 / 16.5) x 100
Percentage yield = 77.576 percent.
What is theoretical yield?
Theoretical yield (also known as predicted yield) is the maximum amount of product that you can get from a reaction.
Theoretical yield is the yield you would get if all the reactants in your experiment turned into a product.
Why is actual yield lower than theoretical yield?
Actual yield is the amount of product you actually get from an experiment. It is rare to get the 100 percent yield in a reaction.
Actual yield is often lower than theoretical yield because:
Some of the reactants don't convert to a product.
Some of the reactants get lost in the air (if it's a gas).
Impurities stop the reaction.
Unwanted by-products get produced in side-reactions.
The reaction reaches equilibrium.
The ideal gas equation
Gases have three natural properties: volume, pressure, and temperature. Scientists have known for a long time that there is a relationship between these three properties. The Ideal Gas Law is an equation that explains the relationship between the natural properties of gases. Here’s how you write the ideal gas equation:
$$ PV\space = nRT $$
P: pressure (Pa)
V: volume \(m^3\)
n: number of moles
R: The gas constant
T: temperature (K)
Calculate the volume of 1 mole of an ideal gas at 0°C and 1 atmosphere pressure.
0° = 273 K
1atm. = 101325 Pa.
R = 8.31441 \(JK^{-1} mol^{-1} \)
PV = nRT
101325 x V = 1 x 8.31441 x 273
V = 2269.83393101325
V = 0.0224 \(m^3\) or 22.4 \(dcm^3\)
Before the ideal gas law, scientists had noticed other relationships between the temperature, pressure, and volume of gases.
What is an ideal gas?
Ideal gases behave according to the Kinetic Gas Theory at all conditions of temperature and pressure.
That means the gas molecules have no volume and no attractive forces between each other. When you think about it, that can't be true at all! So there is no such thing as an ideal gas.
Gases that do not obey kinetic gas theory are called real gases.
Fortunately, most real gases behave in an ideal way.
What is the kinetic theory of gases?
The Kinetic Theory of Gases explains the relationship between the properties of a gas. It describes gases as made up of tiny particles that never stop moving and have plenty of space between them.
This theory is based on a few vital assumptions.
Gases have molecules that move randomly in straight lines.
The molecules of a gas behave like rigid spheres.
When the molecules of gas collide with the sides of a container it causespressure.
When the molecules collide with each other and against the container they donot lose kinetic energy. (The collisions are completely elastic.)
The temperature of the gas relates to the average kinetic energy of its molecules.
The molecules have negligible intermolecular forces between them.
The volume occupied by the molecules is negligible and relative to the volume of the container.
Amount of Substance - Key takeaways
- A mole (n) is the SI unit for the amount of substance. The amount of elementary entities in a mole is equal to the number of atoms in 12g of the carbon-12 isotope. The number of entities per mole is the Avogadro constant.
- The equation for the number of moles is \(n\space\)= \(\frac {m} {M}\) or \(\text{number of moles}\space\) = \(\frac { \text {mass in grams} } {\text {Molar mass}}\)
- Avogadro's constant (L) is the number of atoms in 12 grams of carbon-12 or \(6.022\times 10^{23}\) . We give it the units \(mol^{-1}\) , which you read as "per mole".
- u is the unit of measurement for atomic mass. 1u equals 1/12 the mass of a carbon-12 atom. We compare all atoms to 1/12 of carbon-12 because it equals 1u.
- Relative atomic mass (Ar) is the average mass of all the isotopes of an element, weighed by the abundance of each isotope on Earth.
- Percentage yield measures the effectiveness of a chemical reaction. It tells us how much of our reactants (in percentage terms) successfully turned into a product.
- The formula for percentage yield is \(percentage\space yield\)= \(\frac {actual\space yield} {theoritical\space yield}\times100 \)
- Theoretical yield (also known as predicted yield) is the maximum amount of product that you can get from a reaction.
- Actual yield is the amount of product you actually get from an experiment. It is rare to get the 100% yield in a reaction.
- The ideal gas law is an equation that explains the relationship between the natural properties of gases.
- The ideal gas equation is PV = nRT.
- Ideal gases behave according to the Kinetic Gas Theory at all conditions of temperature and pressure.
- Gases that do not obey kinetic gas theory are called real gases.
- Kinetic theory explains the relationship between the properties of a gas. It is based on the assumption that the molecules have negligible intermolecular forces between them and the volume occupied by the molecules is negligible and relative to the volume of the container.
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