### Video Transcript

In this video, we will learn what
the term atom economy means, the expression used for atom economy using the relative
formula masses of reactants and desired product, and how to calculate atom
economy. We will also learn what the
benefits of a high atom economy are and learn to understand these benefits.

Often, reactions in industry and in
the lab used to produce a specific desired product or target product produce other
products too. Because the other product or
products are not the target substance, we consider them waste products. If we take the amount of the
desired or target product formed as a percentage of all the products produced or
alternatively all the reactants, we get some useful information. We call this the atom economy.

Atom economy can be defined in
several ways, but one way is to say it is the measure of the amount of reactants
which form a desired or useful product. And so atom economy is sometimes
referred to as the atom efficiency. Let’s have a look at the expression
or equation for atom economy.

Atom economy is equal to the total
mass of the desired product or products divided by the total mass of all the
products. And if we multiply by 100 percent,
we can get the answer in terms of a percentage. Because of the law of conservation
of mass — which says that the total mass of all the reactants is equal to the total
mass of all the products — we could replace the term products in the denominator
with the term reactants if we wanted to. In other words, the denominator can
be expressed in terms of the total mass of all the products or the total mass of all
the reactants. We would still get the same answer
for the atom economy.

There is another way to write the
expression for atom economy. Atom economy is also equal to the
total relative formula mass, sometimes called the relative molecular mass, of the
desired product or products divided by the total relative formula mass or relative
molecular mass of all the products. And again, we can multiply by 100
percent to get the answer in a percentage. And as before, we can use the term
reactants instead of products in the denominator because of the law of conservation
of mass. So essentially, there are actually
four ways to express atom economy, either using total mass with the denominator
being total mass of products or reactants or using relative formula mass with the
denominator being for the products or the reactants.

In this lesson, we will use the
expression in the orange rectangle. Note that 𝑀 subscript 𝑟, the
relative formula mass, is sometimes called the relative molecular mass. They have slightly different
definitions technically, but here we will use the term relative formula mass. And this is a unitless
quantity.

Now, let’s have a look at what a
high and a low atom economy means before we look at some problems using the
expression for atom economy. The two pie charts represent the
atom economy produced from two chemical reactions. For the reaction represented by the
pie chart on the left, we see that there was a low atom economy; only 25 percent of
the product was the desired product. And for the reaction represented by
the pie chart on the right, we see that there was a higher atom economy of 60
percent desired product forming.

The portions in orange represent
the unwanted or waste products which formed. For the first reaction, 75 percent
of the products which formed were wasteful or not needed. For the second reaction, only 40
percent of the products which formed were considered to be waste products. Relatively speaking, we can see
that a low atom economy is associated with a high amount of waste and a high atom
economy with a low amount of waste.

Atom economy is becoming
increasingly important as we as a society strive to manufacture goods and chemicals
in a greener, more planet-friendly, and energy-efficient manner. The less waste, especially
hazardous waste, that is produced in a reaction or a process, the less energy is
directed in producing wasteful substances, which are toxic or useless to us. We will discuss the benefits of a
high atom economy a bit further later in the lesson. Now, let’s have a look at some
problems using the expression for atom economy.

Calcium metal can be used to
produce pure rubidium from its chloride according to the equation: Ca solid plus two
RbCl solid reacting to give CaCl2 solid plus two Rb liquid. What is the atom economy for the
production of rubidium by this process, to the nearest percentage unit?

This question asks us to determine
the atom economy for the production of rubidium. Atom economy is a measure of the
amount of starting materials or reactants which are converted to useful or desirable
products. The expression or equation for atom
economy can be expressed in several different ways. One way is to say atom economy is
equal to the total relative formula mass of the desired or useful product or
products divided by the total relative formula mass of all the reactants. And we can multiply by 100 percent
to get the answer in terms of a percentage.

So first we need to determine the
total relative formula mass of the desired product. And in this example, the desired
product is Rb or rubidium. When we calculate the value for the
numerator, we will need to take into account the coefficient of two in front of
rubidium. We will also need to calculate the
total relative formula mass of all the reactants. And the reactants are Ca or calcium
and RbCl, which is rubidium chloride. Again, we will need to take into
consideration the stoichiometric coefficient of two in front of rubidium
chloride.

Let’s clear some space to do the
calculations for the relative formula masses of the substances in the numerator and
in the denominator. So let’s start by calculating the
relative formula mass of the desired product rubidium. Taking into account the coefficient
of two, we can put in the relative formula mass — in this case, just the relative
atomic mass — of rubidium, which is 85.468. And we get this from the periodic
table. We get a value of 170.936, and this
is unitless.

Let’s now do the same calculation
for both of the reactants, calcium and rubidium chloride. Calcium has a mass value of 40.078
from the periodic table. And for rubidium chloride, we will
multiply the values by two because of the coefficient two. Rubidium’s mass value is 85.468,
and chlorine, 35.45 from the periodic table. When we solve, we get 241.836. Now we can use the atom economy
expression and plug in our values into the numerator and denominator.

The total relative formula mass of
the desired product rubidium is 170.936. So we put this in the
numerator. And the total relative formula mass
of all the reactants will be the sum of the relative formula mass of each reactant,
calcium and rubidium chloride, whose mass values we have calculated. Adding the two denominator values,
we get a total value of 281.914. Taking the numerator divided by the
denominator, we get an answer of 60.6 percent, which is the atom economy for the
production of rubidium by this process.

However, the question asks us to
express the answer to the nearest percentage unit. So rounding up, we get an answer of
61 percent. What does this answer mean? The answer tells us that 61 percent
of the starting materials ended up as the useful desired target product,
rubidium. Finally, the atom economy for the
production of rubidium by the process given in the equation is 61 percent.

Let’s have a look at another worked
example.

Sodium azide, NaN3, is an important
compound found in car airbags. One method of producing NaN3 is
shown in the following equation: 2NaNH2 plus N2O reacting to give NaN3 plus NaOH
plus NH3. By calculating the atom economy,
determine the percentage of the wasted starting materials.

The question asks us to calculate
the atom economy. An atom economy is the measure of
the amount of reactants or starting materials which are converted to useful or
target products. They also ask us to determine the
percentage of wasted starting materials. Let’s first calculate the atom
economy of the desired product.

And the desired product in this
example is sodium azide, NaN3. The expression used for atom
economy is the total relative formula mass of the desired product or target product
— in this case, sodium azide — divided by the total relative formula mass of all the
reactants multiplied by 100 percent.

We begin by calculating the
relative formula mass of the desired product, sodium azide. From the periodic table, we get the
atomic mass of sodium of 22.990 and for nitrogen, 14.007, which we will need to
multiply by three because there are three nitrogens in sodium azide, which gives a
relative formula mass for sodium azide of 65.011. And this is a unitless
quantity.

We now have the value for the
numerator in the atom economy expression. Let’s calculate the value for the
denominator. We will need to separately
calculate the relative formula masses for each of the reactants and then add them
together to get the denominator value for the atom economy expression. So for the first reactant, NaNH2,
taking into account the coefficient of two from the balanced equation, we can put in
sodium’s mass, which is 22.990, and nitrogen’s mass of 14.007 and two times the
atomic mass of hydrogen for the two hydrogens in this particular reactant. Solving, we get a relative formula
mass of NaNH2 of 78.026.

For the other reactant, N2O, we
take two times the atomic mass of nitrogen for the two nitrogen atoms and add
oxygen’s atomic mass from the periodic table of 15.999. And we get a value of 44.013. Next, we need to take the sum of
the relative formula masses of each of the reactants. And we get an answer of 122.039,
which is the denominator value in the atom economy expression. Let’s now clear some space and put
in the numerator and denominator values into the atom economy expression.

And we get 65.011 divided by
122.039 timesed by 100 percent, giving an atom economy for sodium azide according to
this process of 53.3 percent to one decimal place. We have now calculated the atom
economy as the question asked. Now, we have to determine the
percentage of the wasted starting materials.

We know that the atom economy of
53.3 percent is the percentage of reactants that were converted into the desired
product. This means that the remainder of
the reactants were not converted to desired product. So the percentage of wasted
reactants or wasted starting materials is equal to 100 percent of the reactants
minus the percent that was converted to desired product, in other words, 100 percent
minus 53.3 percent. And we get an answer of 46.7
percent of wasted starting materials, which were not converted into the desired
product. Finally, the percentage of wasted
starting materials is 46.7 percent.

We know what atom economy is, the
expression for atom economy, and how to calculate it. But what are the benefits of a high
atom economy? We have seen that reactions with a
high atom economy produce little and, in ideal cases, no waste products. This, in turn, allows for
sustainable development as fewer natural resources are used. It could be argued that these
efficient processes often save time and often save money because less time and money
are spent separating products at the end of a reaction and disposing of unwanted
waste. Sometimes, waste is toxic or
hazardous. Researchers and government lawyers
increasingly strive to find ways to make reactions greener by reducing the amount of
waste produced.

In this lesson, we have learned
that atom economy is a measure of the amount of reactants which are converted to a
desired product or products. We saw that there are several
expressions for determining atom economy, one of them being the total relative
formula mass of the desired or target product divided by the total relative formula
mass of all the reactants multiplied by 100 percent. And finally, we saw that a high
atom economy promotes sustainability and produces less waste.