Combustion analysis

Combustion analysis is a reliable method for determining the empirical and molecular formulas of organic compounds that contain carbon, hydrogen, and oxygen. When these compounds undergo complete combustion in an excess of oxygen, they produce carbon dioxide (CO₂) and water (H₂O).

The amounts of CO₂ and H₂O produced allow calculation of the moles of carbon and hydrogen in the original compound, leading to determination of its empirical formula.

Worked example 1 - Calculating empirical formulas from combustion masses

When 9.00 g of an unknown carbonyl compound X is burnt in excess oxygen, it produces 22.0 g of carbon dioxide and 9.00 g of water.

Calculate the empirical formula for this compound.

Step 1: Calculate moles of CO₂

Moles of CO₂ = $\frac{mass}{M_r}=\frac{22.0}{44.0}=0.500$ mol

1 mole of CO₂ contains 1 mole of C, so there are 0.500 moles of C in compound X.

Step 2: Calculate moles of H₂O

Moles of H₂O = $\frac{mass}{M_r}=\frac{9.00}{18.0}$ = 0.500 mol

1 mole of H₂O contains 2 moles of H, so there are 0.500 x 2 = 1.00 moles of H in compound X.

Step 3: Calculate mass of C and H in compound X

Mass of C = n x A_r = 0.500 x 12.0 = 6.00 g

Mass of H = n x A_r = 1.00 x 1.0 = 1.00 g

Step 4: Calculate mass and moles of O in compound X

Mass of O = total mass $-$ (mass of C + mass of H) = 9.00 $-$ (6.00 + 1.00) = 2.00 g

Moles of O = $\frac{mass}{A_r}=\frac{2.00}{16.0}=0.125$ mol

Step 5: Calculate empirical formula

C : H : O mole ratio = $\frac{0.500}{0.125}:\frac{1.00}{0.125}:\frac{0.125}{0.125}=4:8:1$

Therefore, the empirical formula of X is C₄H₈O.

Calculating molecular formulas from combustion reaction volumes

In gaseous reactions, the volumes of the reactants and products can be directly used to determine the molecular formula. This is because all gases at the same temperature and pressure have the same molar volume, allowing us to use the ratio of reacting gas volumes to calculate molar ratios.

Worked example 2 - Calculating molecular formula from combustion volumes

50 cm³ of hydrocarbon Y undergoes complete combustion with 250 cm³ of oxygen, producing 150 cm³ of carbon dioxide.

Determine the molecular formula of Y.

Step 1: Write a balanced equation using the given volumes

50Y + 250O₂ ➔ 150CO₂ + nH₂O

Step 2: Simplify the equation by dividing all coefficients by the coefficient of Y

Y + 5O₂ ➔ 3CO₂ + nH₂O

Step 3: Determine the coefficient for H₂O (n)

5 moles of O₂ react to form 3 moles of CO₂ and n moles of H₂O. Any oxygen atoms not in CO₂ must be in H₂O.

n = (5 × 2) $-$ (3 × 2) = 4

The balanced equation is:

Y + 5O₂ ➔ 3CO₂ + 4H₂O

Step 4: Deduce the molecular formula of Y

All C atoms from Y end up in CO₂, so there are 3 C atoms in Y.

All H atoms from Y end up in H₂O, so there are 8 H atoms in Y.

Therefore, the molecular formula of Y is C₃H₈.

Sequence of techniques for structure determination

After determining the empirical and molecular formulas, chemists employ a series of spectroscopic techniques to progressively reveal the complete structure of an unknown organic compound:

1. Mass spectrometry - Provides the molecular mass and offers clues about structural fragments.
2. Infrared (IR) spectroscopy - Identifies functional groups through their characteristic bond vibrations.
3. Nuclear magnetic resonance (NMR) spectroscopy - Shows the chemical environment and connectivity of hydrogen and carbon atoms.

By integrating the information from these techniques, chemists can deduce the full structure of the compound.

The following examples show how to apply this sequence of techniques to determine the structures of unknown organic compounds.

Worked example 3 - Determining the structure of an organic molecule

Using the following information provided, determine the structure of the unknown organic compound.

• Elemental analysis: C: 60.00%, H: 13.33%, O: 26.67%
• Mass spectrum:

• IR spectrum:

• ¹³C NMR spectrum:

• ¹H NMR spectrum:

Step 1: Elemental analysis and empirical formula calculation

Assuming 100 g of the compound for simplicity, convert the mass percentages to moles:

• Carbon: $\frac{60.00}{12.0}=5.00\text{ mol}$
• Hydrogen: $\frac{13.33}{1.0}=13.33\text{ mol}$
• Oxygen: $\frac{26.67}{16.0}=1.67\text{ mol}$

The smallest number of moles is 1.67. Dividing all by 1.67 gives:

• C: 3, H: 8, O: 1

Empirical formula is C₃H₈O.

Step 2: Molecular formula calculationThe molecular ion peak at m/z = 60 corresponds to the molecular weight of the compound, confirming the empirical formula C₃H₈O as the actual molecular formula.

Step 3: IR spectrum analysisThe broad absorption at 3340 cm^-1 indicates the presence of an -OH group, characteristic of alcohols.

Step 4: NMR spectrum analysis¹³C NMR:

• The peak at δ 64 ppm suggests a carbon bonded to oxygen (C-O).
• The peak at δ 25 ppm suggests a carbon bonded to carbon (C-C).

¹H NMR:

• The septet at δ 4.00 ppm with a relative peak area of 1 is characteristic of a single proton in a unique environment, likely attached to a carbon that is bonded to an OH group.
• The doublet at δ 1.20 ppm with a relative peak area of 6 is characteristic of six protons, suggesting the presence of two methyl groups.

Step 5: Structure determination

Based on all the evidence, the structure can be determined as propan-2-ol.

Worked example 4 - Determining the structure of an organic molecule

Using the following information provided, determine the structure of the unknown organic compound.

• Elemental analysis: C: 54.55%, H: 9.09%, O: 36.36%
• Mass spectrum:

• IR spectrum:

• ¹³C NMR spectrum:

• ¹H NMR spectrum:

Step 1: Elemental analysis and empirical formula calculation

Assuming 100 g of the compound for simplicity, convert the mass percentages to moles:

• Carbon: $\frac{54.55}{12.0}=4.55\text{ mol}$
• Hydrogen: $\frac{9.09}{1.0}=9.09\text{ mol}$
• Oxygen: $\frac{36.36}{16.0}=2.27\text{ mol}$

The smallest number of moles is 2.27. Dividing all by 2.27 gives:

• C: 2, H: 4, O: 1

Empirical formula is C₂H₄O.

Step 2: Molecular formula calculationThe molecular weight from the molecular ion peak (m/z = 88) matches twice the weight of the empirical formula (2 × 44 = 88). Thus, the molecular formula is C₄H₈O₂.

Step 3: IR spectrum analysisThe strong absorption at 1,740 cm^-1 suggests a carbonyl (C=O) group.

Step 4: NMR spectrum analysis¹³C NMR:

• The peak at δ 175 ppm suggests a carbonyl (C=O) carbon.
• The peak at δ 52 ppm suggests a carbon bonded to oxygen (C-O).
• The peak at δ 9 ppm suggests a carbon bonded to carbon (C-C).

¹H NMR:

• The singlet at δ 3.70 ppm with a relative peak area of 3 is characteristic of a methyl group (CH₃) adjacent to an oxygen atom.
• The quartet at δ 2.32 ppm with a relative peak area of 2 is characteristic of a CH₂ group adjacent to a carbonyl group on one side and a methyl group on the other side.
• The triplet at δ 1.15 ppm with a relative peak area of 3 is characteristic of a methyl group (CH₃) adjacent to a CH₂ group.

Step 5: Structure determination

Based on all the evidence, the structure can be determined as methyl propanoate.