Empirical Formula: Videos & Practice Problems

Understanding the difference between empirical and molecular formulas is essential in chemistry. The empirical formula represents the simplest whole number ratio of elements in a compound, derived from the mass percentages of its constituent elements. It reflects the relative number of atoms, not the actual count. Conversely, the molecular formula indicates the exact number of atoms of each element within a compound. For instance, a compound with a molecular formula of:

$C_6{H}_{12}{O}_6$

can have an empirical formula of:

$C_1{H}_2{O}_1$

if the numbers are divisible by a common factor, in this case, 6. However, when no common divisor exists, the empirical formula and the molecular formula are identical. This distinction is crucial when analyzing the composition and calculating the molar mass of substances.

Empirical vs Molecular Formula

The distinction between empirical and molecular formulas is fundamental in understanding chemical compounds. The empirical formula represents the simplest whole number ratio of the elements in a compound, derived from the mass percentages of its constituent elements using the mole concept. This concept facilitates conversions between grams, moles, and units such as molecules, ions, or atoms.

To illustrate, consider the molecular formula C₃H₆O₃. The numbers 3, 6, and 3 can all be divided by 3, leading to the empirical formula CH₂O, which is the reduced form. Similarly, for the molecular formula C₁₀H₁₄N₂, dividing each subscript by 2 yields the empirical formula C₅H₇N. In contrast, the molecular formula C₁₂H₂₂O₁₁ cannot be simplified further, meaning its empirical formula is identical to its molecular formula.

In summary, the molecular formula provides the actual number of each type of atom in a compound, while the empirical formula offers a simplified representation. Understanding this difference is crucial for accurately interpreting chemical compositions and reactions.

Empirical Formula Calculation Example

The empirical formula of a compound represents the simplest whole-number ratio of the elements present. To calculate the empirical formula from the percentages of elements, follow these steps:

First, identify the elements involved and their corresponding symbols from the periodic table. For example, in a compound with 57.47% sodium, 40.01% oxygen, and 2.52% hydrogen, the symbols are Na for sodium, O for oxygen, and H for hydrogen.

Next, convert the percentages into grams by assuming a total mass of 100 grams for the compound. This means that 57.47% sodium translates to 57.47 grams, 40.01% oxygen to 40.01 grams, and 2.52% hydrogen to 2.52 grams.

Then, convert these masses into moles using the atomic masses from the periodic table. The atomic mass of sodium (Na) is approximately 22.99 g/mol, oxygen (O) is about 16.00 g/mol, and hydrogen (H) is roughly 1.008 g/mol. To find the number of moles, divide the mass of each element by its atomic mass:

For sodium: \[\text{Moles of Na} = \frac{57.47 \text{ g}}{22.99 \text{ g/mol}} \approx 2.4998 \text{ moles}\]For oxygen: \[\text{Moles of O} = \frac{40.01 \text{ g}}{16.00 \text{ g/mol}} \approx 2.5006 \text{ moles}\]For hydrogen: \[\text{Moles of H} = \frac{2.52 \text{ g}}{1.008 \text{ g/mol}} \approx 2.5000 \text{ moles}\]

After calculating the moles, divide each mole value by the smallest mole value obtained. In this case, the smallest value is approximately 2.4998 moles of sodium. This results in:

For sodium: \[\frac{2.4998}{2.4998} = 1\]For oxygen: \[\frac{2.5006}{2.4998} \approx 1.0003 \approx 1\]For hydrogen: \[\frac{2.5000}{2.4998} \approx 1.0008 \approx 1\]

Since all values are close to whole numbers, the empirical formula can be directly written as NaOH. If any of the resulting values were not whole numbers or were close to 0.1 or 0.9, rounding would be appropriate. If the values were not easily rounded, you would multiply all ratios by the same factor to achieve whole numbers. For instance, if you had a value of 1.5 for oxygen, you would multiply all ratios by 2 to get 2 sodium, 3 oxygen, and 2 hydrogen, resulting in a different empirical formula.

In summary, the empirical formula derived from the given percentages is NaOH, representing the simplest ratio of sodium, oxygen, and hydrogen in the compound.

Determine the simplest form of a compound made up of carbon, hydrogen, nitrogen and oxygen if it is made of 49.48% C, 5.19% H and 16.48% O.

• A. C₄H₁₂NO₂
• B. C₄H₅N₂O
• C. C₂H₄NO₇
• D. CHN₃O₅

Answer: (B)

A chemist wishing to identify a compound determines the masses of its elements as: 1.445 g S and 6.391 g Cl. Determine its empirical formula.

• A. SCl
• B. S₂Cl₈
• C. SCl₄
• D. SCl₆

Answer: (C)

A compound composed of potassium, manganese and oxygen contains 3.12 g potassium and 1.922 x 10²³ oxygen atoms. If a sample of the compound weighs 12.61 g determine its empirical formula?

• A. KMnO₄
• B. KMnO₂
• C. Mn₂O₉
• D. K₂M₄O₂

Answer: (A)

Here’s what students ask on this topic:

How can I find the empirical formula?

To find the empirical formula, you'll need to follow these steps:

1. Obtain the Masses: Start by determining the mass of each element present in a compound. If you have percentages, assume a 100-gram sample so that your percentages can directly convert to grams.
2. Convert to Moles: Use the atomic masses from the periodic table to convert the mass of each element to moles.
3. Find the Simplest Ratio: Divide the number of moles of each element by the smallest number of moles calculated.
4. Create Whole Numbers: If the ratios aren't whole numbers, multiply all ratios by the smallest number that will convert them into whole numbers (this may be 2, 3, 4, etc.).

The result is the empirical formula, which represents the simplest whole-number ratio of atoms in the compound. Remember that the empirical formula may not necessarily be the same as the molecular formula, which shows the actual number of atoms in a molecule, but it will always be a simplified version of the molecular formula.

What is the empirical formula?

An empirical formula represents the simplest whole-number ratio of elements in a compound. It doesn't provide the exact number of atoms in a molecule, like the molecular formula, but instead shows the simplest ratio of the elements present. For example, the empirical formula for glucose ($C_6{H}_{12}{O}_6$) is ${\mathrm{CH}}_{2}O$, which indicates that for every carbon atom, there are two hydrogen atoms and one oxygen atom.

To determine an empirical formula, you would:

1. Obtain the mass of each element present in a sample of the compound.
2. Convert these masses to moles using the atomic masses from the periodic table.
3. Divide each mole value by the smallest number of moles calculated.
4. Round the resulting ratios to the nearest whole number to get the empirical formula.

If the ratios are not whole numbers, they may be multiplied by a common factor to achieve whole numbers, which will give you the empirical formula of the compound.

How can the empirical formula be found from percent?

To find the empirical formula from percent composition, you need to convert the percentage of each element to moles, then find the simplest whole number ratio of these moles.

Here's a step-by-step process:

1. Convert to Grams: Assume you have 100 grams of the compound. This way, the percentage can directly translate to grams.
2. Convert to Moles: Use the molar mass of each element (from the periodic table) to convert the mass of each element to moles.

$\mathrm{moles}=\frac{\mathrm{mass}\left(g\right)}{\mathrm{molar}\mathrm{mass}(g/\mathrm{mol})}$

3. Find the Simplest Ratio: Divide the number of moles of each element by the smallest number of moles calculated.
4. Make Whole Numbers: If the ratios aren't whole numbers, multiply all ratios by the smallest number that will make them whole.

The resulting whole numbers are the subscripts in the empirical formula. If you end up with a decimal that's very close to a whole number (like 1.5 or 2.5), you'll typically multiply all the numbers by 2 to get whole numbers. The empirical formula represents the simplest whole-number ratio of atoms in the compound.

How can the empirical formula be found from mass?

To find the empirical formula from mass, you first need to convert the mass of each element in a compound to moles by using the atomic masses from the periodic table. Here's a step-by-step guide:

1. Convert Mass to Moles: Divide the mass of each element by its atomic mass to find the number of moles.

For example, if you have 12.0 g of carbon and 32.0 g of oxygen:

• Carbon: 12.0 g / 12.01 g/mol (atomic mass of C) = 1.00 mol
• Oxygen: 32.0 g / 16.00 g/mol (atomic mass of O) = 2.00 mol

2. Determine the Simplest Ratio: Divide the number of moles of each element by the smallest number of moles calculated.

Using the example above:

• Carbon: 1.00 mol / 1.00 mol = 1
• Oxygen: 2.00 mol / 1.00 mol = 2

3. Write the Empirical Formula: Use the ratios to write the subscripts in the empirical formula.

In our example, the empirical formula is $C_1{O}_2$, as the ratio of carbon to oxygen is 1:2.