3 Ways to Determine an Empirical Formula

2024 Author: Samantha Chapman | [email protected]. Last modified: 2024-01-15 13:47

The minimal - or empirical - formula of a compound is the simplest way to write its composition. You should be able to determine that of each compound as long as you know the mass of each element, the percentage masses or the molecular formula.

Steps

Method 1 of 3: with Percentage Masses

Step 1. Look at the data

If you are listing the elements of a compound with percentages instead of grams, you should assume that you are working with exactly 100 g of the substance.

• Below you will find the steps to follow if the hypothesis described above is true. If instead the composition in grams is given, go to the section "with the Masses".
• Example: determines the minimum formula of a substance consisting of 29.3% Na (sodium), 41.1% S (sulfur) and 29.6% O (oxygen).

Step 2. Determine the mass in grams for each element

Assuming that you are working with 100 g of unknown substance, you can establish that the number of grams of each element corresponds to the percentage mentioned by the problem.

Example: per 100 g of unknown compound there are 29.3 g of Na, 41.1 g of S and 29.6 g of O.

Step 3. Convert the mass of each element to moles

At this point, you need this value to be expressed in moles and to do this you need to multiply it by the molar ratio of the respective atomic weight.

• In simple terms, you need to divide each mass by the atomic weight of the element.
• Remember that the atomic weights used for these calculations must be expressed with at least four significant digits.

• Example: for the compound of 29, 3 g Na, 41, 1 g S and 29, 6 g O:

  • 29.3 g Na * (1 mol S / 22.9 g Na) = 1.274 mol Na;
  • 41.1 g S * (1 mol S / 32.06 g S) = 1.282 mol S;
  • 29.6 g O * (1 mol O / 16.00 g O) = 1. 850 mol O.

  

  Step 4. Divide each number of moles by the smallest

  You have to make a stoichiometric comparison between the elements present in the substance, which means that you have to calculate the quantity of each atom in relation to the others that make up the substance; to do this, divide each number of moles by the smallest.

  • Example: the minor number of moles present in the substance corresponds to 1.274 (that of Na, sodium).

    • 1.274 mol Na / 1.274 mol = 1.000 Na;
    • 1.282 mol S / 1.274 mol = 1.006 S;
    • 1. 850 mol O / 1.274 mol = 1.452 O.

    

    Step 5. Multiply the ratios to find the nearest whole number

    The amount of moles present for each element may not be an integer; in cases where small quantities in the order of tenths are involved, this detail does not represent a problem. However, when the value deviates more, you should multiply the ratio to round it to the first whole number.

    • If an element has a ratio close to 0.5, multiply each element by 2; similarly, if one of the ratios is close to 0.25, multiply them all by 4.

    • Example: Since the amount of oxygen (O) is close to 1, 5, you have to multiply each number by 2 to round that of oxygen to an integer.

      • 1,000 Na * 2 = 2,000 Na;
      • 1,006S * 2 = 2,012S;
      • 1.452 O * 2 = 2.904 O.

      

      Step 6. Round the data to the first integer

      Even after the multiplication just described, the amount of moles obtained could still be represented by a decimal value; since no decimal numbers appear in an empirical formula, you need to round off.

      • Example: for previously calculated ratios:

        • 2,000 Na can be written as 2 Na;
        • 2, 012 S can be written as 2 S;
        • 2, 904 O can be written as 3 O.

        

        Step 7. Write the final answer

        Translate the relationships between elements into the standard format used for the minimal formula. The molecular quantity for each element should be subscribed after each chemical symbol (when the number is greater than 1).

        Example: for the compound that contains 2 parts of Na, 2 of S and 3 of O, the minimum formula is: Na₂S.₂OR₃.

        Method 2 of 3: with the Masses

        

        Step 1. Consider the number of grams

        If you are given the composition of an unknown substance with the masses of the various elements expressed in grams, you must proceed as follows.

        • If, on the other hand, the problem reports percentage values, refer to the previous section of the article.
        • Example: determines the empirical formula of an unknown substance consisting of 8, 5 g of Fe (iron) and 3, 8 g of O (oxygen).

        

        Step 2. Transform the mass of each element into moles

        To know the molecular ratio of the elements, you need to convert the masses from grams to moles; to do this, divide the number of grams of each element by its respective atomic weight.

        • From a more technical point of view, you are actually multiplying the mass in grams by the molar ratio based on the atomic weight.
        • Remember that the atomic weight must be rounded to the fourth significant digit to maintain a good level of accuracy in the calculations.

        • Example: in a compound with 8.5 g Fe and 3.8 g O:

          • 8.5 g Fe * (1 mol Fe / 55.85 g Fe) = 0.152 mol Fe;
          • 3.8 g O * (1 mol O / 16.00 g O) = 0.38 mol O.

          

          Step 3. Divide each molar quantity by the smallest number you found

          Determines the number of moles of each element in relation to the elements that make up the substance; to do this, identify the minimum value and use it to divide the others.

          • Example: for the problem under consideration, the lower number of moles is that of iron (0, 152 moles).

            • 0.12 mol Fe / 0.12 mol = 1000 Fe;
            • 0.238 mol O / 0.12 mol = 1.566 O.

            

            Step 4. Multiply the ratios to find the nearest whole number

            Proportional values are often not represented by integers; if the difference is in the order of one tenth, this detail is not a problem. However, when the difference is greater, you have to multiply each value by a coefficient that rounds it to an integer.

            • For example, if the ratio for an item exceeds 0.25, multiply all data by 4; if an element exceeds 0.5, multiply all values by 2.

            • Example: Since the parts of oxygen are equal to 1.566, you have to multiply both ratios by 2.

              • 1,000 Fe * 2 = 2,000 Fe;
              • 1.566 O * 2 = 3.12 O.

              

              Step 5. Round the values to an integer

              When they are only a tenth of an integer, you can round them.

              Example: the ratio of Fe can be written as 2, while that of O can be rounded to 3.

              

              Step 6. Write the final solution

              The relationship between the elements should be transformed into the minimum formula. Each value must be noted as a subscript of the respective symbol, unless it is equal to 1.

              Example: for the substance composed of 2 parts of Fe and 3 of O, the empirical formula is: Fe₂OR₃.

              Method 3 of 3: with the Molecular Formula

              

              Step 1. Evaluate whether subscripts can be reduced to a minimum

              If you have been given the molecular formula of an unknown compound, but you need to find the empirical one, you need to understand if the former can be reduced. Look at the subscripts of each element present; if they all share a common factor (besides 1), you need to proceed to find the minimum formula.

              • Example: C₈H.₁₆OR₈.

              • If, on the other hand, the subscripts are all prime numbers, the molecular formula provided is already in its minimum form.

                Example: Fe₃OR₂H.₇.

                

                Step 2. Find the greatest common divisor of the subscripts

                Write the factors of each number that appears as a subscript of the elements and calculate the greatest common divisor.

                • Example: for C₈H.₁₆OR₈, the subscripts are "4" and "8".

                  • The factors of 8 are: 1, 2, 4, 8;
                  • The factors of 16 are: 1, 2, 4, 8, 16;
                  • The greatest common divisor (GCD) between the two numbers is 8.

                  

                  Step 3. Divide each subscript by the GCD

                  To get the minimum formula, divide all the numbers to the right of each atomic symbol in the formula by the greatest common divisor.

                  • Example: for C₈H.₁₆OR₈:

                    • Divide 8 by the GCD (8) and you get: 8/8 = 1;
                    • Divide 16 by the GCD (8) and you get: 16/8 = 2.

                    

                    Step 4. Write the final answer

                    Replace the original subscripts with those reduced to a minimum. In this way, you have found the empirical formula from the molecular one.

                    • Remember that subscripts equal to 1 are not reported:
                    • Example: C₈H.₁₆OR₈ = CH₂OR.