Determining the Molecular Formula from the Empirical Formula

When faced with an empirical formula and the molecular mass, determining the molecular formula can be a straightforward process. This guide walks you through the steps to find the molecular formula of a compound given its empirical formula and molecular mass. By understanding these steps, you can solve various chemistry problems, especially in the realm of organic chemistry and polymer science.

Understanding the Problem

Consider a compound with an empirical formula of CH and a molecular mass of 28 amu (atomic mass units). The atomic masses of carbon (C) and hydrogen (H) are 12 amu and 1 amu, respectively. Let's explore how to determine its molecular formula.

Step-by-Step Process

1. A. Calculating the Empirical Formula Mass (EFM)

To begin, calculate the empirical formula mass (EFM) of the given empirical formula CH. The EFM is calculated as follows:

$$text{EFM} 12 , text{amu (C)} 1 , text{amu (H)} 13 , text{amu}$$

2. B. Determining the Ratio

The next step is to determine the ratio of the given molecular mass to the EFM. This ratio will tell us by what factor the empirical formula needs to be multiplied to obtain the molecular formula:

$$text{Ratio} frac{text{Molecular Mass}}{text{EFM}} frac{28 , text{amu}}{13 , text{amu}} approx 2.15 $$

3. C. Multiplying the Empirical Formula

Since the ratio is approximately 2.15, we multiply the empirical formula by the closest whole number that makes sense chemically, which is 2:

$$text{Molecular Formula} 2 times text{CH} text{C}_2text{H}_4$$

4. D. Verification

Finally, verify the calculation by summing up the atomic masses in the molecular formula to ensure it matches the given molecular mass:

$$text{Atomic Mass of C}_2text{H}_4 2 times 12 , text{amu (C)} 4 times 1 , text{amu (H)} 24 , text{amu} 4 , text{amu} 28 , text{amu}$$

This confirms that the molecular formula is correct.

General Procedure

Let's generalize the procedure for different compounds with different empirical formulas and molecular masses:

1. CH2

1. Calculate the empirical formula mass:

$$text{EFM} 12 , text{amu (C)} 2 , text{amu (H)} 14 , text{amu}$$

2. Determine the ratio:

$$text{Ratio} frac{28 , text{amu}}{14 , text{amu}} 2$$

3. Multiply the empirical formula:

$$text{Molecular Formula} 2 times text{CH}_2 text{C}_2text{H}_4$$

2. C3H6NO2

1. Calculate the empirical formula mass:

$$text{EFM} 3 times 12 , text{amu (C)} 6 times 1 , text{amu (H)} 14 , text{amu (N)} 2 times 16 , text{amu (O)} 36 6 14 32 88 , text{amu}$$

2. Determine the ratio:

$$text{Ratio} frac{352 , text{amu}}{88 , text{amu}} 4$$

3. Multiply the empirical formula:

$$text{Molecular Formula} 4 times text{C}_3text{H}_6text{NO}_2 text{C}_{12}text{H}_{24}text{N}_4text{O}_8$$

Conclusion

Understanding and applying the concept of empirical and molecular formulas is crucial for solving a variety of chemistry problems, from inorganic to organic chemistry and polymer science. By following the steps outlined, you can reliably determine the molecular formula of any compound given its empirical formula and molecular mass. Practice with different cases to master this essential skill.