# Question Video: Calculating the Energy of an N–H Bond Using Bond Enthalpy Data Chemistry • 10th Grade

Ammonia (NH₃) is a key starting material for the manufacture of fertilizers. The compound is produced by the reaction of nitrogen and hydrogen gases at high temperature and pressure. The energies of selected bonds are given in the table. The total energy change per mole of ammonia produced is −46 kJ/mol. Calculate, to the nearest kJ/mol, the energy of the N–H bond in NH₃.

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### Video Transcript

Ammonia, NH3, is a key starting material for the manufacture of fertilizers. The compound is produced by the reaction of nitrogen and hydrogen gases at high temperature and pressure. The energies of selected bonds are given in the table. The total energy change per mole of ammonia produced is negative 46 kilojoules per mole. Calculate, to the nearest kilojoule per mole, the energy of the NH bond in NH3.

The question describes the reaction between nitrogen and hydrogen gases, which produces ammonia. We can represent this reaction with this balanced chemical equation. We’ve been asked to calculate the energy of the NH bond in NH3. The bond energy, sometimes called the bond enthalpy, is the average amount of energy required to break a particular bond in one mole of gaseous particles.

Breaking bonds requires energy. In other words, the process of breaking bonds is endothermic, and the value of energy is positive. Conversely, forming bonds releases the same amount of energy required to break the bond. So forming a bond is an exothermic process. The energy change of a reaction, Δ𝐻, is the sum of the energy required to break the bonds in reactant molecules and the energy released when bonds in the product molecules are formed.

We know the energy required to break one mole of bonds is the bond energy. And the amount of energy released when one mole of a type of bond is formed is equal to the bond energy, but the value has the opposite sign. So we can sum the bond energies of the bonds in the product molecules and subtract them from the bond energies of the bonds in the reactant molecules.

With this formula, we can solve this problem and calculate the energy of the nitrogen–hydrogen bond. To do the calculation, it’ll be helpful to visualize the bonds involved in this reaction.

The problem says that the total energy change of the reaction is negative 46 kilojoules per mole. This value given is per mole of ammonia produced. There are two moles of ammonia in our reaction equation. So we need to multiply the value we were given by two to get the total change in enthalpy for the reaction. This gives us negative 92 kilojoules per mole for the enthalpy change of the reaction.

In the reactants, there is one nitrogen–nitrogen triple bond, which has a bond energy of 942 kilojoules per mole. There are also three hydrogen single bonds, each with a bond energy of 432 kilojoules per mole. In ammonia, there are three nitrogen–hydrogen bonds. There are two molecules of ammonia giving us a total of six nitrogen–hydrogen bonds. Now we can solve for the energy of the nitrogen–hydrogen bond.

To start off with we can combine these terms on the right-hand side of the equation. Three times 432 gives us 1296. Adding 942 to that gives us 2238 kilojoules per mole. We can isolate the bond energy of the nitrogen–hydrogen bond by subtracting 2238 kilojoules per mole from both sides. This gives us negative 2330 kilojoules per mole on the left-hand side of the equation.

Now, we can solve the problem by dividing both sides of the equation by negative six. This gives us 388.33 repeating kilojoules per mole. The problem told us to report our answer to the nearest kilojoule per mole. So we can round to 388 kilojoules per mole. This gives us our final answer. The energy of the nitrogen–hydrogen bond in ammonia is 388 kilojoules per mole.