Lesson Video: Atom Economy Chemistry

In this video, we will learn how to calculate the atom economy for reactions using the formula masses of the reactants and desired products.

17:45

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.

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