Ammonia is produced industrially from nitrogen and hydrogen according to the equation: $$ \mathrm{N}_{2}+3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3} $$ a. If you are given \(6.2\) moles of nitrogen how many mole of ammonia could you produce? b. How many moles of hydrogen would you need to fully react with \(6.2\) moles of nitrogen? C. If you wished to produce 11 moles of ammonia how many moles of nitrogen would you need to start with?

Chemical reaction equations are not just symbols and numbers thrown together; they represent the blueprint of a chemical reaction. To make sense of these equations, it's important to recognize that they adhere to the law of conservation of mass. This means that the number of atoms for each element must be the same on both sides of the equation.

Take the formation of ammonia (\text{NH}_3), for example, as represented by the equation: \[ \text{N}_2 + 3 \text{H}_2 \rightarrow 2 \text{NH}_3 \]. Each molecule of nitrogen (\text{N}_2) has two nitrogen atoms, and each molecule of hydrogen (\text{H}_2) has two hydrogen atoms. In the end product, each \text{NH}_3 molecule contains one nitrogen atom and three hydrogen atoms. According to the equation, we need three molecules of hydrogen for every molecule of nitrogen to end up with two molecules of ammonia. This adherence to stoichiometric coefficients—1 for \text{N}_2, 3 for \text{H}_2, and 2 for \text{NH}_3—keeps the equation balanced.

The mole concept is a bridge between the micro world of atoms and molecules and the macro world of grams and liters that we interact with daily. A mole is defined as the amount of any substance that contains as many entities (atoms, molecules, ions, or other particles) as there are atoms in 12 grams of pure carbon-12 (\text{C}-12). This magic number is Avogadro's number, approximately \(6.022 \times 10^{23}\).

When we learn that we have 6.2 moles of nitrogen, we are essentially saying we have \(6.2 \times 6.022 \times 10^{23}\) nitrogen molecules at our disposal. This mole concept allows us to translate the microscopic balanced chemical equation into quantities that can be measured and used in the laboratory or industrial processes.

In the textbook exercise, we're looked at how many moles of nitrogen are needed to produce a set amount of ammonia, translating the abstract equation into tangible numbers.

Molar ratio calculations are the heart of stoichiometry, as they quantitatively express the relationship between the amounts of reactants and products in a chemical reaction. In the exercise, for every mole of nitrogen used, two moles of ammonia are produced. Therefore, if you start with 6.2 moles of nitrogen, the molar ratio of \(1 \text{ mole N}_2:2 \text{ moles NH}_3\) tells you that you will end up with twice that amount of ammonia, or 12.4 moles.

To find out how much hydrogen you need, look at the ratio \(1 \text{ mole N}_2:3 \text{ moles H}_2\). With 6.2 moles of nitrogen, you'd multiply by 3 to know you need 18.6 moles of hydrogen. Knowing how to calculate these ratios ensures you can scale reactions up or down and determine the necessary quantities of substances for any chemical process.

Similarly, to know how much nitrogen is needed to produce a certain amount of ammonia, you use the inverse of the original ratio, which in this case is \(2 \text{ moles NH}_3:1 \text{ mole N}_2\). For 11 moles of ammonia, you divide by 2, which tells you that you need 5.5 moles of nitrogen. By mastering molar ratio calculations, you can convert between moles of different substances involved in a chemical reaction with confidence.