Atomic tally

When we refer to a chemical equation as balanced, we mean that the appropriate coefficients have been used to show the same number of atoms of each element on both the product and reactant sides of the arrow. If you understand conservation of matter, then you would expect the number of atoms that appear on each side of the chemical equation to be the same. In fact, we must have the same number of atoms of each of the elements, on each side of the chemical equation. To check to see if that is true, you may want to perform what I will call an atomic tally. Tally up the number of atoms of each element on each side of the equation, and make sure that they are the same, as demonstrated in Figure 6-la. 

For this lesson, it will be important for you to master the skill of the atomic tally. You will need to be able to check if an equation is balanced before you can learn how to balance them correctly. Let s try a couple of examples where you can do an atomic tally, before you check the answers. The first example that we will look at represents a chemical reaction that you may conduct in chemistry, as it is a common process for generating hydrogen gas in the lab. 

Do an atomic tally for the following equation and determine if it is balanced. 

Try to do an atomic tally for Example 1 before checking your answer. See if our answers match. 

Did we get the same answers Do you notice that this chemical equation doesn t show any coefficients Sometimes, a chemical equation is balanced when all of the substances have a coefficient of 1. When the coefficient for a substance is 1, we don t write it, and the 1 is understood. If you are ever asked to balance a chemical reaction that is already balanced, with no coefficients written in, simply write, Already balanced, and your instructor will know that you did your atomic tally correctly. 

Let s try another example. Can you do the atomic tally for the next example ... 

How can we be sure that this is the correct balanced equation We can do another atomic tally and make sure that the same number of atoms of each element appear on both sides of the equation. 

Let s try another example. Do an atomic tally for the following equation. If the equation is not balanced, figure out what coefficient(s) you need to add in order to achieve balance. Finally, do another atomic tally to make sure that the new equation is balanced. 

Do an atomic tally for the following equation and determine if it is balanced. If not, balance the equation using coefficients, and repeat the tally. 

First, we do an atomic tally to see if our equation is already balanced. 

We notice that our equation is not balanced. The number of carbon atoms on each side of the equation is the same, but we have twice as many hydrogen atoms on the left-hand side, and there is an additional oxygen atom on the right-hand side. Let s start by adding a coefficient of 2 to the water on the product side, in an attempt to balance the hydrogen atoms. Then, we will do another atomic tally to see where we are. To make this easier to follow, I will put the coefficients that I add in bold and italics. 

Do you see how the skills of performing an atomic tally and balancing equations go hand in hand To be able to do one, you need to be able to do the other. Let s try one more example together. Take a look at Example 4 and see how far you can go before you check my answer. 

In the first step, I will do an atomic tally to get an idea of what to do next. 

The equation is technically balanced, as you can show with an atomic tally, but it is still not correct. Because all of the coefficients are reducible by the number 2, you must divide each coefficient by 2, leaving you with this equation ... 

Do an atomic tally for each of the following equations and state whether or not they are balanced as shown. 

The equation shows an atom of potassium transforming into an atom of calcium and an additional particle that we haven t learned yet. When we discussed creating an atomic tally to balance a chemical equation in Lesson 6-1, we said that you must have the same number of atoms of each... 

HC1 + Ca(OH)2 -> CaCl2 + 2HzO]—The atomic tally showed that we only had 3 hydrogen on the reactant side, and 4 on the product side. By adding a coefficient of 2 to the hydrogen chloride, the entire equation balanced out. 

In the mixed quantum-classical molecular dynamics (QCMD) model (see [11, 9, 2, 3, 5] and references therein), most atoms are described by classical mechanics, but an important small portion of the system by quantum mechanics. The full quantum system is first separated via a tensor product ansatz. The evolution of each part is then modeled either classically or quan-tally. This leads to a coupled system of Newtonian and Schrbdinger equations. 

A quick tally of the atoms indicates that all are balanced. Mentally, you should go through a process similar to the chart in Table 11.4. 

There are roughly 421 reports of homoleptic bis(dithiolene) units based on transition metal elements. The approximate tally of the structures as a function of central metal atom is outlined in Fig. 2. The examples predominantly contain late transition metals. The majority of complexes are Ni based, partially because of interest in these complexes for materials applications. Other common central elements are Cu, Pd, Pt, Au, and Zn. There are also a few Fe and Co complexes and a small number of structures based on Cr, Mn, Ag, Cd, and Hg. 

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