Question Video: Calculating the Total Number of Atoms of an Element in a Complex Formula Chemistry

How many atoms of oxygen are present in the formula 10 SO₂?


Video Transcript

How many atoms of oxygen are present in the formula 10SO2?

Recall a chemical formula is defined as an expression of chemical symbols and numerical subscripts that represents the composition of one unit of a compound. Rewriting the formula given in the question, we have the compound SO2, where the chemical symbol S indicates the presence of the element sulfur and the chemical symbol O indicates the presence of the element oxygen. Both chemical symbols can be found on the periodic table.

The chemical symbol for oxygen and the chemical symbol for sulfur can be found in group 16, with oxygen’s chemical symbol present in period two and sulfur’s chemical symbol in period three of the periodic table. If we take a look at the subscripts for each chemical symbol in the formula, first we will notice there is not a subscript shown for sulfur. This is because a rule when writing chemical formulas is that subscript values equal to one are implied but not written in the chemical formula. In other words, when there is one atom of any element in a given chemical formula, the subscript value number one is not shown, only the chemical symbol is.

So in the case of the sulfur atom in this chemical formula, though there is no subscript shown in the formula provided, according to the rule, there is actually an implied number one, which means there is one sulfur atom in one molecule of this compound. As for the oxygen atom, the subscript two indicates there are two oxygen atoms in one molecule of this compound.

This can also be observed in drawing the ball-and-stick model of an SO2 molecule, which depicts one central sulfur atom bonded to two oxygen atoms. Based on this information, one might be tempted to say the answer to “How many oxygen atoms are in the formula 10SO2?” is two oxygen atoms because of the subscript two to the right of the oxygen chemical symbol. However, this would be incorrect in this case because there is one more piece of information provided in this formula that we have not yet discussed.

The numeral 10 present at the beginning of the formula is called a coefficient. Coefficients appear in front of the chemical formula and indicate the number of discrete units. Or in this specific case, it indicates the number of SO2 molecules, which means there are 10 molecules of SO2 in this formula. To solve this problem, let’s start by listing the information we have learned about the formula. The coefficient number 10 in front of the SO2 molecule indicates there are 10 molecules of SO2. Because the question is focused on the number of oxygen atoms, we will write out that one molecule of SO2 has two oxygen atoms in it.

Now we can rewrite these two pieces of information as fractions in order to solve for the total number of oxygen atoms in the formula. When the information is written as such, it allows for the units of molecules SO2 to cancel out, which means we are left with units of oxygen atoms, which matches what the question is asking for. If we complete the algebraic function by multiplying the two numbers on top of the fractions and dividing that product by all the numbers on the bottom of the fractions, we will find there are 20 oxygen atoms in the formula 10SO2.

Another way to solve this problem would be to distribute the coefficient 10 to the implied subscript one to the right of the sulfur chemical symbol and to the subscript two to the right of the oxygen chemical symbol. Upon multiplying the coefficient 10 to the subscript two, we obtain the same answer of 20 oxygen atoms in 10 molecules of SO2. This is also verified by drawing 10 molecules of SO2, where upon counting up the oxygen atoms, we can see that with two oxygen atoms in each molecule, 10 molecules of SO2 equals 20 oxygen atoms.

Therefore, the answer to this question is there are 20 oxygen atoms in the formula 10SO2.

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