Video: Determining the Percentage of the Wasted Starting Materials Used to Produce Sodium Azide (NaN_3) Using Atom Economy Calculations

Sodium azide (NaN₃) is an important compound found in car airbags. One method of producing NaN₃ is shown in the following equation. 2NaNH₂ + N₂O ⟶ NaN₃ + NaOH + NH₃. By calculating the atom economy, determine the percentage of the wasted starting materials.

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Video Transcript

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.

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