Video Transcript
The estimated electron affinities for successive additions of electrons in an atom of phosphorus are listed below. A phosphorus atom plus an electron produces a P1− ion with an electron affinity of positive 72 kilojoules per mole. A P1− ion plus an electron produces a P2− ion with an electron affinity of negative 468 kilojoules per mole. A P2− ion plus an electron produces a P3− ion with an electron affinity of negative 886 kilojoules per mole. What is the total energy change for the formation of the P3− ion, where a phosphorus atom plus three electrons produces a P3− ion?
This is a question about electron affinity. Electron affinity is defined as the energy released when an atom or ion gains an electron. When a neutral atom gains an electron, like in the first example here, the amount of energy that is released is called the first electron affinity. When we add a second electron, turning a one minus ion into a two minus ion, the amount of energy that’s released is called the second electron affinity. The third example shows the energy released when we add an electron to a P2− ion to make a P3− ion. This amount of energy is the third electron affinity for phosphorus.
Sometimes the terms electron affinity and first electron affinity are used interchangeably. In that case, we would not see the word ion included in its definition. This question is asking about the total energy change of the formation of the P3− ion. The equation at the bottom of the screen shows a neutral phosphorus atom gaining three electrons to form that ion. The beginning set of three equations also shows a starting phosphorus atom turning into a P3− ion. Instead of adding three electrons at once, the electrons are added individually, one in each of the three equations.
If we wanna know how much energy is released when we add three electrons to the phosphorus atom, we can simply add up the amount of energy released as we add each individual electron. If we carry out this arithmetic, we will arrive at an answer of negative 1282 kilojoules per mole released in total. We have not yet reached our final answer. This number is the amount of energy released in this process. But the question is asking for the energy change. Let’s investigate this difference.
If energy is released, it means that there is a negative energy change. In other words, the amount of energy in the system goes down. On the other hand, if energy is absorbed, that means there’s a positive energy change. Energy is entering the system. So the amount of energy is increasing.
Our calculations show that we are releasing a negative amount of energy. In this case, we’ve run into a double negative. Releasing a negative amount of energy is the same as gaining energy or absorbing energy. So, to match what is going on during this process, we need to write the energy change of the formation of the ion as a positive number, positive 1282 kilojoules per mole, the correct answer. So what is the total energy change for the formation of the P3− ion? That’s a positive 1282 kilojoules per mole.
