1.2. Empirical and Molecular Formulas

The chemical formula of a compound provides essential information about the types and numbers of atoms present. There are two main types of chemical formulas: empirical and molecular.

Chemical formulas are symbolic representations of compounds that tell us what elements are present and in what quantities. The two primary types of formulas are:

1. Empirical Formula: This formula shows the simplest whole-number ratio of atoms of each element in the compound.
2. Molecular Formula: This formula indicates the actual number of atoms of each element in a molecule. It is often a multiple of the empirical formula.

Think of a cake recipe. The empirical formula is like the ratio of ingredients (e.g., 2 cups flour to every 1 cup sugar), while the molecular formula tells you the exact amount needed for a specific recipe (e.g., for one cake, you use 2 cups of flour and 1 cup of sugar).

Determining Empirical Formula from Composition by Mass:

1. Assume a 100 g sample, so that percentages can be directly converted to masses in grams.
2. Convert the mass of each element to moles using its molar mass.
3. Divide the number of moles of each element by the smallest number of moles calculated. This will give a ratio, where at least one element has a subscript of 1.
4. If the resulting ratios are not whole numbers, multiply all the ratios by the smallest integer that converts them into whole numbers.

To determine the empirical formula based on the composition by mass of a compound, follow these steps:

1. Assume 100 g: Convert percentages to grams (for example, 40% becomes 40 g).
2. Convert to Moles: Use the molar masses of the elements to convert grams into moles.
3. Calculate Ratios: Find the smallest number of moles and use it to create ratios for each element.
4. Whole Number Ratios: If any ratios are fractions, convert them to whole numbers by multiplying by an appropriate factor.

Imagine you have a bag of mixed nuts containing 40% almonds, 30% cashews, and 30% walnuts. Assuming a 100 g bag, you have 40 g almonds, 30 g cashews, and 30 g walnuts. You would convert these amounts into 'nut portions' (moles) based on their respective weights to figure out the simplest way to represent your mix.

Example: A compound contains 40.0% Carbon, 6.7% Hydrogen, and 53.3% Oxygen by mass.

1. Masses: C = 40.0 g, H = 6.7 g, O = 53.3 g
2. Moles:
   • C: 40.0 g / 12.01 g mol⁻¹ ≈ 3.33 mol
   • H: 6.7 g / 1.01 g mol⁻¹ ≈ 6.63 mol
   • O: 53.3 g / 16.00 g mol⁻¹ ≈ 3.33 mol
3. Divide by smallest (3.33):
   • C: 3.33 / 3.33 = 1
   • H: 6.63 / 3.33 ≈ 1.99 ≈ 2
   • O: 3.33 / 3.33 = 1
4. Empirical Formula: CH₂O

Let's go through the example step by step:

1. Start with a 100 g sample: You already have the masses based on percentages.
2. Convert to Moles: Use the molar mass for each element to find out how many moles are present.
3. Calculate Ratios: Take your smallest mole value and divide all moles by that to find the simplest ratio.
4. Final Empirical Formula: The resulting subscripts give you the empirical formula, which in this case is CH₂O.

Think of making a smoothie where you have different fruits. If you have 40 g of bananas, 6.7 g of strawberries, and 53.3 g of yogurt, you would calculate the amount of each fruit per your serving size, find a ratio, and use it to write down a simplified recipe that represents your smoothie.

To determine the molecular formula, you need both the empirical formula and the molar mass of the compound.

1. Calculate the empirical formula mass (EFM) by summing the relative atomic masses in the empirical formula.
2. Determine the integer 'n' by dividing the experimental molar mass (M) of the compound by the empirical formula mass (EFM): n = M / EFM
3. Multiply the subscripts in the empirical formula by 'n' to get the molecular formula.

To find the molecular formula:

1. Calculate Empirical Formula Mass (EFM): Add the atomic masses of each element in the empirical formula.
2. Find 'n': Use the formula n = M / EFM to find how many times the empirical formula fits into the molar mass.
3. Molecular Formula: Scale the empirical formula by this integer to get the molecular formula.

If your smoothie recipe (empirical formula) calls for 1 banana for every 2 strawberries, and you want to make enough smoothie for a party (molecular formula), you multiply your recipe: if you determine you need 6 bananas and 12 strawberries, that gives you the larger recipe that fits your needs.

Example (continuing from above): If the molar mass of the compound (with empirical formula CH₂O) is 180.18 g mol⁻¹.

1. EFM (CH₂O) = 30.03 g mol⁻¹
2. n = 180.18 / 30.03 ≈ 6
3. Molecular Formula = (CH₂O)₆ = C₆H₁₂O₆ (Glucose)

In this example:

1. First, you calculate the empirical formula mass (EFM) of CH₂O, which is 30.03 g/mol.
2. Next, to find 'n', you divide the given molar mass (180.18 g/mol) by the EFM. This gives you n ≈ 6.
3. Finally, you multiply the subscripts in the empirical formula by 6 to arrive at the molecular formula C₆H₁₂O₆.

Returning to our smoothie, if you found that to serve a large group you need to scale your recipe up six times, where the original recipe calls for 1 banana, 2 strawberries, and 1 yogurt, your final recipe would then be 6 bananas, 12 strawberries, and 6 yogurts for the big batch!

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