Hydrogen peroxide H2O2 is a highly reactive material used as a bleaching agent and rocket fuel. The compound slowly decomposes in the presence of light to form water and oxygen. The equation for this reaction is shown. The total energy change per mole of oxygen formed is negative 210 kilojoules per mole. 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 oxygen-to-oxygen single bond in H2O2.
In this question, we are given a balanced chemical equation for the decomposition of hydrogen peroxide. We are also given the value of the change in enthalpy of this reaction, which is negative 210 kilojoules per mole. The negative sign indicates that the decomposition reaction is exothermic, which means that energy is released to the surroundings when the reaction takes place. To solve this problem, we will need to use the balanced chemical equation and the enthalpy change of the reaction to help us calculate the bond energy of the oxygen-to-oxygen single bond in the hydrogen peroxide molecules.
We are also provided a table listing the bond energy for two bonds. Bond energy, which we will abbreviate as BE in this video, is the average amount of energy required to break a specific bond in one mole of gaseous molecules. We will make use of this table a little bit later on in the video. For now, let’s clear some space to begin working on the problem.
During a chemical reaction, certain bonds in the reactant molecules break. In order for bonds to be broken, energy must be absorbed from the surroundings. In fact, bond energy is the specific amount of energy that must be absorbed for a particular bond to break. New chemical bonds must form to make the product molecules. And the formation of these new bonds releases energy. We can make use of the following equation to help us solve the problem. The overall enthalpy change of the reaction, Δ𝐻, is equal to the sum of the bond energies of the bonds broken in the reactants minus the sum of the bond energies of the bonds formed in the products. In other words, the enthalpy change of a reaction is the difference between the amount of energy absorbed to break bonds and the amount of energy released when new bonds form.
Now, we need to determine which bonds in the reactant molecules are broken during the reaction. The coefficient two written in front of the hydrogen peroxide molecule means two molecules are reacting. Let’s go ahead and draw two molecules. We notice that in order to form two water molecules, the oxygen-to-oxygen single bonds in the hydrogen peroxide molecules must be broken. In addition, one oxygen-to-hydrogen single bond in each molecule must also be broken. Let’s note this now below our equation. In order to complete the formation of two water molecules, two new oxygen-to-hydrogen single bonds must form. Finally, the two oxygen atoms that were not incorporated into the water molecules form a double bond to produce the molecule of oxygen.
Let’s record the three bonds formed in the products below our equation. Now, we’re ready to perform our calculation. We know the enthalpy change of the reaction is negative 210 kilojoules per mole. Since in this problem, we are trying to find the bond energy of the oxygen-to-oxygen single bond, let’s represent these two bonds as two 𝑥. Next, according to the table, the bond energy of two oxygen-to-hydrogen single bonds will be two times 473 kilojoules per mole. Now, we can substitute these same values for the oxygen-to-hydrogen single bonds that form in the products. Finally, we’ll use 494 kilojoules per mole for the bond energy of the oxygen-to-oxygen double bond.
Now that we have substituted all of the bond energy values, we need to solve for 𝑥. After simplifying what’s inside each set of brackets, we get the following equation, which we can simplify further by subtracting 1440 kilojoules per mole from 946 kilojoules per mole. The resulting equation is negative 210 kilojoules per mole equals two 𝑥 minus 494 kilojoules per mole.
After adding 494 kilojoules per mole to both sides of the equation, we get positive 284 kilojoules per mole equals two 𝑥. To solve for 𝑥, we need to divide both sides of the equation by two. Finally, this gives us positive 142 kilojoules per mole equals 𝑥. Therefore, the energy of the oxygen-to-oxygen single bond in H2O2 to the nearest kilojoule per mole is 142 kilojoules per mole.