Molar Ratio Examples

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:

2H_{2}+ O_{2}---> 2H_{2}O

I will use it for the first three examples.

**Example #1:** What is the molar ratio between H_{2} and O_{2}?

**Solution:**

The ratio is two-to-one. The 2 is the coefficient in front of the H_{2}and the 1 is the coefficient understood to be in front of the O_{2}. Here is the ratio in fractional form:Make sure you also can recognize a ratio when it's written using a colon:

2 –– 1 2:1The 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 O_{2} and H_{2}O?

**Solution:**

The ratio is one-to-two. The 1 is in front of the O_{2}and the 2 is in front of the H_{2}O. As a fraction, it is:The colon form is, of course:

1 –– 2 1:2Another way to see a ratio written is like this:

1 is to 2

**Example #3:** What is the molar ratio between H_{2} and H_{2}O?

**Solution:**

The ratio is: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, from time to time, reduce the ratio to one-to-one and, sooner or later, someone would ask where the one-to-one ratio came from.

2 –– 2 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.

You have been warned!

**Example #4:** (a) What is the molar ratio between O_{3} and O_{2}? (b) What is the molar ratio between O_{2} and O_{3}?

2O_{3}---> 3O_{2}

**Solution:**

For (a), it is:

And the answer to (b) simply reverses the numbers:

2 –– 3

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

3 –– 2

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:** N_{2} + 3H_{2} ---> 2NH_{3}

Write the molar ratios for (a) N_{2} to H_{2} and (b) NH_{3} to H_{2}.

**Solution:**

The ratio for (a) is:and the ratio for (b) is:

1 –– 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.

2 –– 3

**Example #6:** 2SO_{2} + O_{2} ---> 2SO_{3}

Write the molar ratios for (a) O_{2} to SO_{3} and (b) SO_{2} to SO_{3}.

**Solution:**

(a) is:and (b) is:

1 –– 2

2 –– 2

**Example #7:** PCl_{3} + Cl_{2} ---> PCl_{5}

Write the molar ratios for (a) PCl_{3} to Cl_{2} and (b) PCl_{3} to PCl_{5}.

**Solution:**

Both requested ratios are this:

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

**Example #8:** 4NH_{3} + 3O_{2} ---> 2N_{2} + 6H_{2}O

Write the molar ratios for (a) NH_{3} to N_{2} and (b) H_{2}O to O_{2}.

**Solution:**

(a):

4 –– 2 (b):

6 –– 3 Note that both ratios can be reduced.

Eventually, ratios like the above 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:** Fe_{2}O_{3} + 3CO ---> 2Fe + 3CO_{2}

Write the molar ratios for (a) CO to CO_{2} and (b) Fe to CO.

**Solution:**

(a):

3 –– 3

(b):

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

**Example #10:** In this equation:

C_{2}H_{6}O + 3O_{2}---> 2CO_{2}+ 3H_{2}O

what is the mole ratio between O_{2} and H_{2}O?

(a) 1:1; (b) 3:2; (c) 2:3; (d) 3:3

**Solution:**

From the coefficients of the equation, the mole ratio is 3:3. However, this reduces to a 1:1 ratio. That means that answer choice (a) would be considered by most teachers to be the correct answer.Please note that using a 3:3 ratio in a calculation is equivalent to using a 1:1 ratio. The same answer is obtained using 3:3 as opposed to using 1:1.

The ChemTeam, when in the classroom (now retired), would use the unreduced ratio in calculations done for teaching purposes. This is because, invariably, if the reduced ratio is used, the question would be asked: "Where did the 1:1 ratio come from?"

**Example #11:** Given the balanced equation:

2SO_{2}+ O_{2}---> 2SO_{3}

what is the mole ratio of O_{2} to SO_{3}?

(a) 2:1; (b) 1:2; (c) 2:2; (d) 2:3

**Solution:**

The correct answer is (b) 1:2.When I saw this problem on Yahoo Answers, the first answer given was 2:1, the reverse of the correct answer. 2:1 is the molar ratio of SO

_{3}to O_{2}.Make sure to write the numbers of the ratio in the same order as used in the question. The first substance mentioned goes in the numerator, the second mentioned in the denominator.

**Example #12:** What is the molar ratio between copper(II) sulfate and water in the following compound?

CuSO_{4}⋅5H_{2}Ocopper(II) sulfate pentahydrate

**Solution:**

Notice that this is not a chemical reaction, it is simply a chemical formula of a hydrate. Remember, hydrates have a fixed amount of water per mole of the non-water compound.In this example, the molar ratio is 1:5. For every one mole of CuSO

_{4}, there are five moles of water.

**Example #13:** What is the molar ratio between the anhydrous compound and water for the following hydrates?

(a) CuCl_{2}⋅2H_{2}O

(b) MgSO_{4}⋅H_{2}O

(c) Cr_{2}(SO_{4})_{3}⋅18H_{2}O

**Solution:**

(a) 1:2 ---> one mole of CuCl_{2}and two of water

(b) 1:1 ---> one mole of MgSO_{4}and one of water

(c) 1:18 ---> one mole of Cr_{2}(SO_{4})_{3}and eighteen of water

**Example #14:** What is the molar ratio between potassium carbonate and water in the following compound?

K_{2}CO_{3}⋅1.5H_{2}O ---> named potassium carbonate sesquihydrate

**Solution:**

The ratio is 1 to 1.5. In chemistry, there is a desire to state ratios as small whole numbers, so this ratio would be expressed as 2 to three and this formula could be written:2K

_{2}CO_{3}⋅3H_{2}OThere is nothing whatsoever wrong with the 1 to 1.5 ratio. It's just that there is a desire within the chemistry community to use ratios expressed as small whole numbers.

**Example #15:** What is the molar ratio between calcium sulfate and water in the following compound?

CaSO_{4}⋅0.5H_{2}O ---> named calcium sulfate hemihydrate

**Solution:**

In small whole numbers, the ratio is 2:1 and the formula can be written thusly:2CaSO

_{4}⋅H_{2}O