### Molar Ratios

The molar ratio will assume a place of central importance in solving stoichiometry problems. The sources for these ratios are the coefficients of a balanced equation. We will look at what a molar ratio is and then a brief word on how to recognize which ratio to use in a problem.

The ChemTeam's favorite sample equation is:

2H2 + O2 ---> 2H2O

I will use it for the first three examples.

Example #1: What is the molar ratio between H2 and O2?

Solution:

The ratio is two-to-one. Here is the ratio in fractional form:
$\frac{2}{1}$

Make sure you also can recognize a ratio when it's written using a colon:

2:1

The ChemTeam recommends you always explicitly write the numeral one when it is in the denominator of the ratio.

Example #2: What is the molar ratio between O2 and H2O?

Solution:

The ratio is one-to-two. As a fraction, it is:
$\frac{1}{2}$

The colon form is, of course:

1:2

Another way to see a ratio written is like this:

1 is to 2

Example #3: What is the molar ratio between H2 and H2O?

Solution:

The ratio is:
$\frac{2}{2}$

As you well know, this reduces to a one-to-one (or 1:1) ratio. For lessons that follow, the ChemTeam will mostly use the unreduced fraction. The reason is this: in the classroom, the ChemTeam would often reduce the ratio to one-to-one and, sooner or later, someone would ask where the one-to-one ratio came from.

As the difficulty level of the problems goes up, the ChemTeam will just use the reduced ratio (assuming you have mastered the earlier materials, such as in this present tutorial). Also be aware, as you examine a solution to a problem by someone else, they may just use the reduced ratio without saying anything about it.

Be aware!

Example #4: (a) What is the molar ratio between O3 and O2? (b) What is the molar ratio between O2 and O3?

2O3 ---> 3O2

Solution:

The first one:

$\frac{2}{3}$

And the second simply reverses the numbers:

$\frac{3}{2}$

As you can see, the exact molar ratio you would use depends on how the problem is worded.

However, a warning: people tend to play fast and loose with the molar ratio. The ChemTeam tends to put the first substance mentioned into the numerator. However, other people can be more haphazard. What they do is write a ratio without an explanation for how it got to be that way. What you have to do is figure out from context which number is associated with which substance. You do that by looking at the coefficients of the balanced equation.

Before looking at the following examples, an important point: the coefficients of a reaction only give the ratio in which substances react. They do not in any way tell you HOW MUCH is reacting. This point is elaborated upon in what the ChemTeam believes is the next logical unit from here. However, look at the remaining examples first!

Example #5: N2 + 3H2 ---> 2NH3

Write the molar ratios for N2 to H2 and NH3 to H2.

Solution:

The first ratio is:
$\frac{1}{3}$

and the second is:

$\frac{2}{3}$

Sometimes, a student will gather the mistaken impression that the molar ratio can only be constructed using the reactants of a given equation. The molar ratio can be constructed using any two compounds in the reaction, be they reactants or products.

Example #6: 2SO2 + O2 ---> 2SO3

Write the molar ratios for O2 to SO3 and SO2 to SO3.

Solution:

The first is:
$\frac{1}{2}$

and the second is:

$\frac{2}{2}$

Example #7: PCl3 + Cl2 ---> PCl5

Write the molar ratios for PCl3 to Cl2 and PCl3 to PCl5.

Solution:

Both requested ratios are this:
$\frac{1}{1}$

As the problems get more complex, there will be an interesting error students make when using a 1:1 ratio.

Example #8: 4NH3 + 3O2 ---> 2N2 + 6H2O

Write the molar ratios for NH3 to N2 and H2O to O2.

Solution:

Both ratios can be reduced. They are:
$\frac{4}{2}$

and

$\frac{6}{3}$

Eventually, these ratios will be used in calculations. You may use the unreduced ratio or the reduced ratio in the actual calculation. The ChemTeam's position is that it doesn't matter and so NEVER deducted points if the unreduced ratio was used. However, there are teachers who insist on the reduced ratio being used. Make sure you know what your teacher wants you to do.

Example #9: Fe2O3 + 3CO ---> 2Fe + 3CO2

Write the molar ratios for CO to CO2 and Fe to CO.

Solution:

$\frac{3}{3}$

and

$\frac{2}{3}$

Notice that I stopped mentioning things like two-to-four and 2:4. Also, a reminder that you might see something like this:

two is to four