Video Transcript
Chloromethane is produced by the reaction of methane, CH4, with chlorine gas in the presence of UV light. The equation for this reaction is shown. The reaction of 1.00 mole of methane releases 104 kilojoules of energy. The energies of selected bonds in the reactants and products are given in the table. Calculate, to the nearest kilojoule per mole, the energy of the C-Cl bond.
Before solving the problem, let’s ensure that the provided chemical equation is balanced. We need to count up the number of each type of atom on either side of the equation. On the reactants side of the equation, there are four hydrogen atoms in the methane molecule. On the products side, there are three hydrogen atoms in the chloromethane molecule plus an additional hydrogen atom in hydrogen chloride for a total of four hydrogen atoms. So the hydrogen atoms are currently balanced in the equation.
Let’s take a look at the carbon atoms. There is one carbon atom in the methane molecule on the reactants side. And on the products side, there is one carbon atom in the chloromethane molecule. So the carbon atoms are also balanced. Finally, let’s take a look at the chlorine atoms. On the reactants side, there are two chlorine atoms. And on the products side, there is one chlorine atom in chloromethane plus an additional chlorine atom in hydrogen chloride for a total of two chlorine atoms. So we’ve confirmed that the provided equation is a balanced chemical equation.
Now, we need to examine which specific bonds in the reactant molecules are broken during the reaction and what new bonds are formed. By examining the reactant and product molecules closely, we notice that one carbon-to-hydrogen single bond in the methane molecule is broken and a new carbon-to-chlorine single bond is formed to produce a chloromethane molecule. In addition, the chlorine-to-chlorine single bond in diatomic chlorine must also have broken so that one chlorine atom forms a bond in the chloromethane molecule and the second chlorine atom forms a single bond with hydrogen to make a hydrogen chloride molecule.
We are also provided a table that lists the bond energy, or BE, for three of the bonds that we identified in the equation. Bond energy, also known as bond enthalpy, is the average amount of energy needed to break a bond in one mole of molecules. This question is asking us to calculate the bond energy of the carbon-to-chlorine single bond specifically, which is not given in the table. However, we do know that the reaction releases 104 kilojoules of energy for every one mole of methane that reacts. This energy is known as the change in bond enthalpy for the reaction and is represented by the symbol △𝐻. When a reaction releases energy, it is considered exothermic, so we’ll need to use a negative sign. The bond enthalpy for this reaction would be written as negative 104 kilojoules per mole.
Recall that to calculate the change in bond enthalpy, we’ll need to sum up the bond energies for all the bonds that are broken and subtract off the sum of the bond energies for the bonds that are formed. Remember that breaking bonds absorbs energy and forming new bonds releases energy. So the difference between these amounts of energy is the change in bond enthalpy. The two bonds broken during the reaction are the carbon-to-hydrogen single bond and the chlorine-to-chlorine single bond. The two new bonds formed during the reaction are the carbon-to-chlorine single bond and the hydrogen-to-chlorine single bond.
Now, we can substitute the bond energy values from the table into our equation. Breaking the carbon-to-hydrogen single bond requires 411 kilojoules per mole, and breaking the chlorine-to-chlorine single bond requires 240 kilojoules per mole. The bond energy for the carbon-to-chlorine single bond is what we’re trying to solve for. And 428 kilojoules per mole is released when the hydrogen-to-chlorine single bond forms. After adding 411 kilojoules per mole into 240 kilojoules per mole, we get 651 kilojoules per mole absorbed to break bonds. As for the bonds formed, the subtraction sign outside of the brackets means that we need to subtract off the bond energy for the C-to-Cl bond and subtract off the 428 kilojoules per mole.
Now, we’re ready to combine like terms. Let’s subtract 428 kilojoules per mole from 651 kilojoules per mole. The right side of our equation is now 223 kilojoules per mole minus the bond energy for the carbon-to-chlorine bond. Next, we’ll need to subtract 223 kilojoules per mole from both sides of our equation. This gives us the following new equation. Negative 327 kilojoules per mole is equal to the negative of the bond energy of the C-Cl bond. Bond energy is always a positive value, so let’s divide both sides of our equation by negative one. This gives us the answer 327 kilojoules per mole as the energy for the carbon-to-chlorine single bond.
