EMPIRICAL, MOLECULAR FORMULAS AND PERCENTAGE COMPOSITION BY MASS

EMPIRICAL, MOLECULAR FORMULAS

The molecular formula is an expression of the number and type of atoms that are present in a single molecule of a substance. It represents the actual formula of a molecule.

Subscripts after element symbols represent the number of atoms. If there is no subscript, it means one atom is present in the compound.

The empirical formula is also known as the simplest formula. The empirical formula is the ratio of elements present in the compound.

The subscripts in the formula are the numbers of atoms, leading to a whole number ratio between them.

Examples of Molecular and Empirical Formulas

The molecular formula of glucose is C₆H₁₂O₆. One molecule of glucose contains 6 atoms of carbon, 12 atoms of hydrogen and 6 atoms of oxygen.

If you can divide all of the numbers in a molecular formula by some value to simplify them further, then the empirical or simple formula will be different from the molecular formula. The empirical formula for glucose is CH₂O. Glucose has 2 moles of hydrogen for every mole of carbon and oxygen. The formulas for water and hydrogen peroxide are:

• Water Molecular Formula: H₂O
• Water Empirical Formula: H₂O
• Hydrogen Peroxide Molecular Formula: H₂O₂
• Hydrogen Peroxide Empirical Formula: HO

In the case of water, the molecular formula and empirical formula are the same.

Finding Empirical and Molecular Formula from Percent Composition

Percent (%) composition = (element mass/compound mass) X 100

If you are given the percent composition of a compound, here are the steps for finding the empirical formula:

1. Assume you have a 100 grams sample. This makes the calculation simple because the percentages will be the same as the number of grams. For example, if 40% of the mass of a compound is oxygen then you calculate you have 40 grams of oxygen.
2. Convert grams to moles. Empirical formula is a comparison of the number of moles of a compound so you need your values in moles. Using the oxygen example again, there are 16.0 grams per mole of oxygen so 40 grams of oxygen would be 40/16 = 2.5 moles of oxygen.
3. Compare the number of moles of each element to the smallest number of moles you got and divide by the smallest number.
4. Round your ratio of molesto the nearest whole number as long as it is close to a whole number. In other words, you can round 1.992 up to 2, but you can’t round 1.33 to 1. You’ll need to recognize common ratios, such as 1.333 being 4/3. For some compounds, the lowest number of atoms of an element might not be 1! If the lowest number of moles is four-thirds, you will need to multiply all ratios by 3 to get rid of the fraction.
5. Write the empirical formula of the compound. The ratio numbers are subscripts for the elements.

Finding the molecular formula is only possible if you are given the molar mass of the compound. When you have the molar mass you can find the ratio of the actual mass of the compound to the empirical mass.

If the ratio is one (as with water, H₂O), then the empirical formula and molecular formula are the same. If the ratio is 2 (as with hydrogen peroxide, H₂O₂), then multiply the subscripts of the empirical formula by 2 to get the correct molecular formula. two.

Steps for Determining an Empirical Formula

1. Start with the number of grams of each element, given in the problem.
   • If percentages are given, assume that the total mass is 100 grams so that

the mass of each element = the percent given.

1. Convert the mass of each element to moles using the molar mass from the periodic table.
2. Divide each mole value by the smallest number of moles calculated.
3. Round to the nearest whole number.  This is the mole ratio of the elements and is

represented by subscripts in the empirical formula.

1. • If the number is too far to round (x.1 ~ x.9), then multiply each solution by the same

factor to get the lowest whole number multiple.

1. • • e.g.  If one solution is 1.5, then multiply each solution in the problem by 2 to get 3.
     • e.g.  If one solution is 1.25, then multiply each solution in the problem by 4 to get 5.

Once the empirical formula is found, the molecular formula for a compound can be determined if the molar mass of the compound is known.

simply calculate the mass of the empirical formula and divide the molar mass of the compound by the mass of the empirical formula to find the ratio between the molecular formula and the empirical formula.  Multiply all the atoms (subscripts) by this ratio to find the molecular formula.

Example Problem #1

A compound was analyzed and found to contain 13.5 g Ca, 10.8 g O, and 0.675 g H.  What is the empirical formula of the compound?

Start with the number of grams of each element, given in the problem.

Convert the mass of each element to moles using the molar mass from the periodic table.

Divide each mole value by the smallest number of moles calculated.  Round to the nearest whole number.

This is the mole ratio of the elements and is represented by subscripts in the empirical formula.

Example Problem #2

NutraSweet is 57.14% C, 6.16% H, 9.52% N, and 27.18% O.  Calculate the empirical formula of NutraSweet and find the molecular formula.  (The molar mass of NutraSweet is 294.30 g/mol)

Start with the number of grams of each element, given in the problem.

• If percentages are given, assume that the total mass is 100 grams so that
  the mass of each element = the percent given.

Convert the mass of each element to moles using the molar mass from the periodic table.

Divide each mole value by the smallest number of moles calculated.  Round to the nearest whole number.

This is the mole ratio of the elements and is represented by subscripts in the empirical formula.

• If the number is too far to round (x.1 ~ x.9), then multiply each solution by the same
  factor to get the lowest whole number multiple.

Now, we can find the molecular formula by finding the mass of the empirical formula and setting up a ratio:

Percentage Composition

• Percentage composition of a compound is a ratio of an amount of each element to the total amount of individual elements in a compound, which is then multiplied with 100.
• Let us take an example of H2O i.e. Water. Water has 2 molecules of hydrogen, and one mole of water is of 18.0152 grams. And one mole of a hydrogen atom is of 1.008 grams.
• So, 2 hydrogen moles weighs 2.016 grams. Hence, one mole of water has 2.016 grams of hydrogen mole. Therefore, the percentage composition of hydrogen would be 2.016/18.0152 = 11.19%. Now let us study in detail about Percentage composition and its formula.

What is Percentage Composition?

The percentage composition of a given compound is nothing but the ratio of the amount of each element to the total amount of individual elements present in the compound. We then multiply this value by 100. Here, we measure the quantity in terms of grams of the elements present in the solution.

The percent composition of any compound is an expression of its composition in terms of all the elements present. The significance of this composition calculation is found in the chemical analysis.

The Formula for Percentage Composition

We can express the percentage composition of a given element using the formula below:

• Here, % C_E is the percentage composition of the element E. This is the value that we are going to calculate. The numerator on the right side indicates the total amount of element E present in the compound. On the other hand, the denominator is an expression for the total amount of all the elements present in the compound.
• We multiply this ratio by 100 to get the percentage form of the composition. Let us now look at the mass percentage of composition in more details. We will also look at its importance.

Learn more about Atomic mass and molecular mass.

Mass Percentage Composition

• We use the concept of mass percentage composition to denote the concentration of an element in a compound or a component in a mixture. We use this term to signify the total percent by mass of each element that is present in a compound.
• It is important to note that we can calculate the mass percentage composition by dividing the mass of a component by the total mass of the mixture. This ratio is then to be multiplied by 100. We also call it the mass percent(w/w) %.

Importance of Mass Percentage

• For many scientific and practical reasons, we ought to know what quantity of an element is present in a given compound. This is indispensable for the chemists to get to the empirical formula of many compounds.
• This formula helps in showing the lowest whole number of moles and the relative number of atoms of each element in a compound. With the help of the empirical formula, chemists can also calculate the actual molecular formula. This formula shows the exact number of atoms in the compound.

Determining the Mass Percent from a Chemical Formula

• We will explain this section with the help of an example. It will clear your fundamentals on how to calculate the mass percent. Let us consider glucose. The formula for glucose is C₆H₁₂O₆. Let us calculate the mass percent of each of the elements in glucose.
• From the formula, we can see the number of moles of each of the elements. Glucose has 6 carbon atoms, 12 hydrogen atoms and also 6 oxygen atoms. Let us now multiply each of the atoms by its molar mass. Thus, we arrive at the mass of each of the element in glucose.
• We now divide each mass by mass of 1 mole of glucose to arrive at the mass fraction of each element. Multiplying this value by 100 gives the mass percentage of the elements.

The Example in Detail

• Each mole of carbon has a mass of 12.01g/mol of carbon. This, we know, from the periodic table. So, 6 moles of carbon will have 12.01g/mol x 6 = 72.06g of Carbon. Similarly, 1 mole of Hydrogen has a mass of 1.008g/mol of Hydrogen. Therefore, 12 moles of Hydrogen will have the mass of 12 x 1.008 = 12.096g of Hydrogen.
• Going by the same logic for Oxygen, 1 mole of oxygen has a mass of 16.00g/mol. Therefore, 6 moles of oxygen will have 16.00 x 6 = 96 g of Oxygen. Thus, 1 mole of Glucose (C₆H₁₂O₆) has a total mass of 72.06 +12.096 + 96 = 180.16 g/mol

Calculating the Mass Percentage.

• To find out the mass % of the three elements of glucose, let us first calculate the mass fraction of each element in 1 mole of glucose. So, what do we mean by the mass fraction? It is the mass that each element contributes to the total mass of glucose. By multiplying this by 100, we get the mass percentage of each element.

Mass fraction of Carbon = 72.06g/180.16g = 0.4000
Therefore, mass % of Carbon= 0.4000×100 = 40.00%
Mass fraction of Hydrogen = 12.096/180.16 = 0.06714
Therefore, mass % of Hydrogen= 0.06714 x 100 = 6.714%
Mass fraction of Oxygen =96/180.16 = 0.53286
Therefore, mass% of Oxygen = 0.53286 x 100 = 53.286%

It is interesting to note that even if carbon and oxygen have an equal number of moles of the compound, their mass percentages are different. Oxygen has a higher value in this as its molar mass is higher than that of carbon.

Learn how to calculate the number of Moles and Equivalent weight here.

Solved Example For You

Q: Find the percent composition of each element in water.

Solution: We know that the chemical formula for water is H₂O. Let us now calculate the molar mass of water. The molar mass of Oxygen = 16.00 × 1 = 16 g/mole and of Hydrogen = 1.01 × 2 = 2.02 g/mole

Now, using the molar mass of each of the given elements, we find out the percentage composition of each element in H₂O. It is given as the ratio of the grams of the element to the grams of the total element in the compound, multiplied by 100. Calculating the percentage composition of Hydrogen,

% H = 2.02/18.02 × 100
Therefore, % H= 11.21 %
Calculating the percentage composition of Oxygen,
Therefore, % O = 16/18.02 ×100 = 88.79 %

CALCULATING PERCENTAGE COMPOSITION EXPLAINED

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