Video Transcript
Using the diagram and the standard enthalpies of formation in the given table, what is the standard enthalpy of reaction for the decomposition of phosphorus pentachloride?
In this question, we are provided a diagram called an energy cycle or reaction cycle. The cycle consists of three different chemical reactions. Let’s number these three reactions. There’s also an enthalpy change associated with each reaction in the cycle. We can use the following chart to keep track of the reactions and their enthalpy changes. Our job in solving this problem is to determine the standard enthalpy of reaction, or 𝛥𝐻 r, for the decomposition of phosphorus pentachloride. The chemical formula of phosphorus pentachloride is PCl5. Reaction one represents the decomposition of phosphorus pentachloride to form phosphorus trichloride, or PCl3, and chlorine gas, or Cl2.
We need to determine the standard enthalpy of this reaction. The standard enthalpy of reaction is the enthalpy change of a reaction that is measured at standard conditions when substances are in their standard states. In the provided table, we have also been given the standard enthalpies of formation of two of the substances involved in reaction number one. The standard enthalpy of formation is the enthalpy change when one mole of substance is formed from its constituent elements in their standard states and under standard conditions. At the bottom of the reaction cycle are the elements phosphorus and chlorine in their standard states. Reaction two represents the formation of one mole of PCl5 from its constituent elements phosphorus and chlorine in their standard states.
According to the data table, the enthalpy change for this reaction is negative 399 kilojoules per mole. The arrow for reaction number three is pointing toward both PCl3 and Cl2. Therefore, reaction three represents the formation of one mole of PCl3 and one mole of Cl2 from their elements in their standard states. According to the data table, the standard enthalpy of formation of just PCl3 is negative 306 kilojoules per mole. But the enthalpy of formation for chlorine gas is zero kilojoules per mole because an element in its standard state has a standard enthalpy of formation of zero. This means that the overall enthalpy change for reaction three is negative 306 kilojoules per mole.
We can use the enthalpy changes of reactions two and three to calculate the enthalpy change of reaction one. Hess’s law states that the enthalpy change for a reaction is independent of the path taken. So as long as the starting and ending points of the other reactions in the energy cycle are the same as reaction one, then we can add together their enthalpy changes to determine the enthalpy change of reaction one. The starting point of our alternative path through the reaction cycle is at PCl5.
To proceed through the reaction cycle, we need to reverse reaction number two. Whenever we reverse a reaction, we need to change the sign of the enthalpy change. So the enthalpy change for reaction two is now positive 399 kilojoules per mole. The next step in the reaction cycle is to complete reaction three in the direction it is written. This allows us to have the same end point as reaction one. Now, we’re ready to add these two enthalpy changes together. The enthalpy change of reaction one is equal to positive 399 kilojoules per mole plus negative 306 kilojoules per mole.
Therefore, the standard enthalpy of reaction for the decomposition of phosphorus pentachloride is positive 93 kilojoules per mole.
