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.