6.3: Mole Relationships and Chemical Equations
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Learning Objectives
 To use a balanced chemical reaction to determine molar relationships between the substances.
Previously, you learned to balance chemical equations by comparing the numbers of each type of atom in the reactants and products. The coefficients in front of the chemical formulas represent the numbers of molecules or formula units (depending on the type of substance). Here, we will extend the meaning of the coefficients in a chemical equation.
Consider the simple chemical equation
\[\ce{2H_2 + O_2 → 2H_2O}\]
The convention for writing balanced chemical equations is to use the lowest wholenumber ratio for the coefficients. However, the equation is balanced as long as the coefficients are in a 2:1:2 ratio. For example, this equation is also balanced if we write it as
\[\ce{4H_2 + 2O_2 → 4H_2O}\]
The ratio of the coefficients is 4:2:4, which reduces to 2:1:2. The equation is also balanced if we were to write it as
\[\ce{22H_2 + 11O_2 → 22H_2O}\]
because 22:11:22 also reduces to 2:1:2.
Suppose we want to use larger numbers. Consider the following coefficients:
\[12.044 \times 10^{23}\; H_2 + 6.022 \times 10^{23}\; O_2 → 12.044 \times 10^{23}\; H_2O\]
These coefficients also have the ratio 2:1:2 (check it and see), so this equation is balanced. But 6.022 × 10^{23} is 1 mol, while 12.044 × 10^{23} is 2 mol (and the number is written that way to make this more obvious), so we can simplify this version of the equation by writing it as
\[\ce{2 \;mol\; H_2 + 1\; mol\; O_2 → 2 \;mol\; H_2O}\]
We can leave out the word mol and not write the 1 coefficient (as is our habit), so the final form of the equation, still balanced, is
\[\ce{2H_2 + O_2 → 2H_2O}\]
Now we interpret the coefficients as referring to molar amounts, not individual molecules. The lesson? Balanced chemical equations are balanced not only at the molecular level but also in terms of molar amounts of reactants and products. Thus, we can read this reaction as “two moles of hydrogen react with one mole of oxygen to produce two moles of water.”
2 molecules H_{2 } 1 molecule O_{2} 2 molecules H_{2}O
2 moles H_{2} 1 mole O_{2} 2 moles H_{2}O
2 x 2.02 g=4.04 g H_{2} 32.0 g O_{2 }2 x 18.02 g=36.04 g H_{2}O
Figure \(\PageIndex{1}\): This representation of the production of water from oxygen and hydrogen show several ways to interpret the quantitative information of a chemical reaction.
By the same token, the ratios we constructed to describe molecules reaction can also be constructed in terms of moles rather than molecules. For the reaction in which hydrogen and oxygen combine to make water, for example, we can construct the following ratios:
\[\mathrm{\dfrac{2\: mol\: H_2}{1\: mol\: O_2}\: or\: \dfrac{1\: mol\: O_2}{2\: mol\: H_2}}\]
\[\mathrm{\dfrac{2\: mol\: H_2O}{1\: mol\: O_2}\: or\: \dfrac{1\: mol\: O_2}{2\: mol\: H_2O}}\]
\[\mathrm{\dfrac{2\: mol\: H_2}{2\: mol\: H_2O}\: or\: \dfrac{2\: mol\: H_2O}{2\: mol\: H_2}}\]
We can use these ratios to determine what amount of a substance, in moles, will react with or produce a given number of moles of a different substance. The study of the numerical relationships between the reactants and the products in balanced chemical reactions is called stoichiometry. The ratio of coefficients in a balanced chemical equation, used in computations relating amounts of reactants and products is called the stoichiometric factor.
Example \(\PageIndex{1}\)
How many moles of oxygen react with hydrogen to produce 27.6 mol of H_{2}O? The balanced equation is as follows:
\[\ce{2H2 + O2 > 2H2O} \nonumber\]
Solution
Because we are dealing with quantities of H_{2}O and O_{2}, we will use the stoichiometric ratio that relates those two substances. Because we are given an amount of H_{2}O and want to determine an amount of O_{2}, we will use the ratio that has H_{2}O in the denominator (so it cancels) and O_{2} in the numerator (so it is introduced in the answer). Thus,
\(\mathrm{27.6\: mol\: H_2O\times\dfrac{1\: mol\: O_2}{2\: mol\: H_2O}=13.8\: mol\: O_2}\)
To produce 27.6 mol of H_{2}O, 13.8 mol of O_{2} react.
Exercise \(\PageIndex{1}\)
Using 2H_{2} + O_{2} → 2H_{2}O, how many moles of hydrogen react with 3.07 mol of oxygen to produce H_{2}O?
 Answer

\(\mathrm{3.07\: mol\: O_2\times\dfrac{2\: mol\: H_2}{1\: mol\: O_2}=6.14\: mol\: H_2}\)
Concept Review Exercise

How do we relate molar amounts of substances in chemical reactions?
Answer

Amounts of substances in chemical reactions are related by their coefficients in the balanced chemical equation.
Key Takeaway
 The balanced chemical reaction can be used to determine molar relationships between substances.
Exercises

List the molar ratios you can derive from this balanced chemical equation:
NH_{3} + 2O_{2} → HNO_{3} + H_{2}O

List the molar ratios you can derive from this balanced chemical equation
2C_{2}H_{2} + 5O_{2} → 4CO_{2} + 2H_{2}O

Given the following balanced chemical equation,
6NaOH + 3Cl_{2} → NaClO_{3} + 5NaCl + 3H_{2}O
how many moles of NaCl can be formed if 3.77 mol of NaOH were to react?

Given the following balanced chemical equation,
C_{5}H_{12} + 8O_{2} → 5CO_{2} + 6H_{2}O
how many moles of H_{2}O can be formed if 0.0652 mol of C_{5}H_{12} were to react?

Balance the following unbalanced equation and determine how many moles of H_{2}O are produced when 1.65 mol of NH_{3} react.
NH_{3} + O_{2} → N_{2} + H_{2}O

Trinitrotoluene [C_{6}H_{2}(NO_{2})_{3}CH_{3}], also known as TNT, is formed by reacting nitric acid (HNO_{3}) with toluene (C_{6}H_{5}CH_{3}):
HNO_{3} + C_{6}H_{5}CH_{3} → C_{6}H_{2}(NO_{2})_{3}CH_{3} + H_{2}O
Balance the equation and determine how many moles of TNT are produced when 4.903 mol of HNO_{3} react.

Chemical reactions are balanced in terms of molecules and in terms of moles. Are they balanced in terms of dozens? Defend your answer.

Explain how a chemical reaction balanced in terms of moles satisfies the law of conservation of matter.
Answers

1 mol NH_{3}:2 mol O_{2}:1 mol HNO_{3}:1 mol H_{2}O

3.14 mol

4NH_{3} + 3O_{2} → 2N_{2} + 6H_{2}O; 2.48 mol
6. 3HNO_{3} + C_{6}H_{5}CH_{3} → C_{6}H_{2}(NO_{2})_{3}CH_{3} + 3H_{2}O; 1.634 mol
7. Yes, they are still balanced.
8. A chemical reaction, balanced in terms of moles, contains the same number of atoms of each element, before and after the reaction. This means that all the atoms and its masses are conserved.