If you've been given a homework assignment where you need to figure out the empirical formula for a compound, but you have no idea how to start, fear not! wikiHow is here to help! First, take a look at the basic knowledge you need to have to get it, and then move on to the example in the second part.
Steps
Part 1 of 2: Understanding the Basics
Step 1. Understand what the empirical formula is
In chemistry, it's the simplest way to describe a compound: basically, it's a list of the elements that make up a compound, organized by their percentage. It is important to note that this simple formula does not describe the arrangement of the atoms within the compound; it limits itself to stating which elements it is made up of. For instance:
A compound that is 40.92% carbon, 4.58% hydrogen and 54.5% oxygen will have an empirical formula of C3H.4OR3 (in the second part we will see, through an example, how to derive the empirical formula of this compound).
Step 2. Understand the expression 'percentage composition'
The 'percentage composition' refers to the percentage of each individual atom in the whole compound we are considering. To derive the empirical formula of a compound, we need to know its percentage composition. If you need to find the empirical formula as a homework assignment, you will most likely be given percentages.
In a chemistry laboratory, to find the percentage composition, the compound would be subjected to some physical tests and then to a quantitative analysis. Unless you're in a lab, you won't need to actually do these tests
Step 3. You will be dealing with gram-atom
A gram-atom is the specific quantity of an element equal to a number of grams equal to its atomic mass. To find a gram atom, the equation is: the percentage of the element in the compound (%) divided by the element's atomic mass.
For example, suppose we have a compound made up of 40.92% carbon. The atomic mass of carbon is 12, so our equation will be 40.92 / 12 = 3.41
Step 4. Learn how to find the atomic ratio
When you find yourself working with a compound, you have to calculate more than one gram atom. After you have found all the gram atoms in the compound, look at them all. To derive the atomic ratio, you will need to identify the smallest gram-atom of all the ones you have calculated. Then you will divide all your gram atom by the smallest gram atom. For instance:
- Let's say we are working with a compound that has three gram-atoms: 1, 5, 2 and 2, 5. The smallest gram-atom of these three numbers is 1, 5. So, to find the atomic ratio, you have to divide all of them. the numbers for 1, 5 and then separate them with the ratio symbol :
- 1, 5/1, 5 = 1. 2/1, 5 = 1, 33. 2, 5/1, 5 = 1, 66. So your atomic ratio is 1: 1, 33: 1, 66.
Step 5. You need to understand how to convert atomic ratio numbers to integers
When writing an empirical formula, you need whole numbers. This means that you can't use a number like 1.33. After you get your atomic ratio, you need to convert every decimal number (like, precisely, 1.33) to an integer (like 3). To do this, you need to find an integer that can be multiplied by every single number in your atomic ratio. For instance:
- Try 2. Multiply the numbers in your atomic ratio (1, 1, 33 and 1, 66) by 2. Get 2, 2, 66 and 3, 32. Since they are not integers, 2 does not go Well.
- Try the 3. Multiplying 1, 1, 33 and 1, 66 by 3, you get 3, 4 and 5. Consequently, your atomic ratio in integers is 3: 4: 5.
Step 6. You must understand what these integers mean to the empirical formula
In fact, the whole number ratio we just calculated is part of the empirical formula. These three whole numbers are the small numbers that we find hanging on the foot of each letter that represents a distinct element of the compound. For example, our invented empirical formula would look like this:
X3Y4Z5
Part 2 of 2: Derive the Empirical Formula
Step 1. Determine the percentage composition of your compound
If you're trying to find the empirical formula for a homework assignment, you'll likely be given the percentage composition - you just need to know where to look. For instance:
- Let's say the assignment asks you to look at a sample of vitamin C. It lists: 40.92% carbon, 4.58% hydrogen, 54.5% oxygen. This is the percentage composition.
- 40.92% of vitamin C is made up of carbon, while the rest is 4.58% hydrogen and 54.5% oxygen.
Step 2. Find the number of gram-atoms present in the compound
As noted in the first part, the equation for deriving the number of gram-atoms is: the percentage of the element in the compound (%) divided by the atomic mass of the element itself.
In our example, the atomic mass of carbon is 12, that of hydrogen is 1, while for oxygen it is 16.
- Number of gram-atoms of carbon = 40.92 / 12 = 3.41
- Number of gram-atoms of hydrogen = 4.58 / 1 = 4.58
- Number of gram-atoms of oxygen = 54.50 / 16 = 3.41
Step 3. Calculate the atomic ratio
Find the smallest gram atom we just calculated. In our example, it is 3.41 (of both carbon and hydrogen: they both have the same value). You must then divide all gram atom values by this number. You will write the report like this: carbon value: hydrogen value: oxygen value.
- Carbon: 3.41 / 3.31 = 1
- Hydrogen: 4.58 / 3.41 = 1.34
- Oxygen: 3.41 / 3.31 = 1
- The atomic ratio is 1: 1, 34: 1
Step 4. Convert the ratio to integers
If your atomic ratio is made up of whole numbers, you can skip this step. In our example, however, we need to convert 1.34 to an integer. The smallest integer that can be multiplied with the numbers in our atomic ratio to get whole numbers is 3.
- 1 x 3 = 3 (this is fine, because 3 is an integer).
- 1.34 x 3 = 4 (4 is also an integer).
- 1 x 3 = 3 (again, 3 is an integer).
- Our ratio in whole numbers is therefore carbon (C): hydrogen (H): oxygen (O) = 3: 4: 3
Step 5. Write the empirical formula
To do this, you just have to write the letters of each component, in this case C for carbon, H for hydrogen and O for oxygen, with their numerical equivalents to the subscript. In our example, the empirical formula is:
C.3H.4OR3
Advice
- The molecular formula represents the total number of elements present, while the empirical formula represents the smallest ratio between the atoms of each element.
- If you were to obtain the percentage composition in the laboratory, you could perform spectrometric tests on the sample of the compound.
