Combustion Analysis: Empirical and Molecular Formulas

Key concepts

• Moles are part of the count and reflect the ratio of atoms in a sample, not the exact number of atoms. The mole ratio equals the atom ratio in the formula for the compound.
• Empirical formula: the simplest whole-number ratio of atoms for a compound (e.g., C:H:O in a hydrocarbon with oxygen).
• Combustion analysis setup: burn a sample (containing C, H, O) in excess O₂ so all C and H convert to CO₂ and H₂O; use these products to deduce the original amounts of C, H, and O in the sample.
• If the combustion is done with excess O₂, the oxygen atoms in CO₂ and H₂O come partly from the sample and partly from the atmospheric O₂; mass balance is used to determine how much O came from the sample.
• The molecular formula is a multiple of the empirical formula; determine the multiplier by comparing the compound’s molar mass to the empirical formula mass.
• Practical workflow: always write the combustion equation first to stay organized; then insert the given data and compute step-by-step.

Key equations and how to use them

• Moles of carbon from combustion products:
  $n<em>C = n</em>{CO_2}$
• Moles of hydrogen from combustion products:
  $n<em>H = 2\,n</em>{H_2O}$
• Mass balance to find oxygen in the original sample:
  • Mass of carbon in the sample:
    $m<em>C = n</em>C \cdot M<em>C\quad (M</em>C = 12.01\ \text{g/mol})$
  • Mass of hydrogen in the sample:
    $m<em>H = n</em>H \cdot M<em>H\quad (M</em>H = 1.008\ \text{g/mol})$
  • Total mass of the sample: $m_{tot}$ (given)
  • Mass of oxygen in the sample:
    $m<em>O = m</em>{tot} - (m<em>C + m</em>H)$
  • Molar mass of oxygen:
    $M_O = 16.00\ \text{g/mol}$
  • Moles of oxygen in the sample:
    $n<em>O = \frac{m</em>O}{M_O}$
• Build the mole ratio and derive the empirical formula:
  • Form the ratio by dividing all moles by the smallest value among (nC, nH, nO): $\text{ratio} = \left(\frac{n</em>C}{n<em>{min}},\ \frac{n</em>H}{n<em>{min}},\ \frac{n</em>O}{n_{min}}\right)$
  • If fractions appear, multiply all by a common factor to obtain whole numbers (e.g., if you get 0.5, 0.5, 1, multiply by 2 to get 1, 1, 2).
  • Remember to report the empirical formula in the order C:H:O. Example from the transcript: if you obtain 1, 2, 1 for C:H:O, the empirical formula is CH₂O.
• Converting to the molecular formula:
  • Compute the empirical formula mass:
    $M<em>{emp} = \sum</em>i n<em>i M</em>i$
  • Compare to the actual molar mass of the compound (given or measured): $M_{mol}$
  • Determine the multiplier:
    $n = \frac{M<em>{mol}}{M</em>{emp}}$
  • The molecular formula is the empirical formula multiplied by this integer n: if n is an integer, the molecular formula is ((empirical)_n).
  • Example: empirical CH₂O has mass $M_{emp} = 12.01 + 2(1.008) + 16.00 \approx 30.03\ \text{g/mol}$; if the actual molar mass is 60.06 g/mol, then $n = \frac{60.06}{30.03} = 2$ and the molecular formula is C₂H₄O₂.

Step-by-step workflow for combustion data

• Step 1: Write the combustion reaction schema: a hydrocarbon containing C, H, and possibly O combusts with excess O₂ to form CO₂ and H₂O.
  • General expectation: hydrocarbon (or vanillin-like compound) + O₂ (excess) → CO₂ + H₂O. Always check if the problem specifies an oxygen-rich environment to guarantee complete combustion.
• Step 2: Use measured CO₂ to determine carbon content:
  • From CO₂ moles, get C moles: $n<em>C = n</em>{CO_2}$
• Step 3: Use measured H₂O to determine hydrogen content:
  • From H₂O moles, get H moles: $n<em>H = 2\,n</em>{H_2O}$
• Step 4: Determine how much oxygen came from the sample by mass balance:
  • Compute masses: $m<em>C = n</em>C M<em>C, \quad m</em>H = n<em>H M</em>H$
  • If total mass of the sample is known: $m<em>O = m</em>{tot} - (m<em>C + m</em>H)$
  • Then $n<em>O = m</em>O / M_O$
• Step 5: Form the empirical formula from the mole ratios and ensure integers by scaling if needed.
• Step 6: If you know the molecular molar mass, compute the empirical mass and scale to the molecular formula as described.

Worked notes on the transcript content

• The transcript emphasizes that moles reflect ratios, not exact counts, and that the empirical formula is the simplest integer ratio of atoms.
• It shows an example where the mole ratios come out as 3.33 : 3.33 : 6.67, which, when divided by the smallest value (3.33), yields 1 : 1 : 2. Interpreting this in C:H:O order gives CH₂O as the empirical formula.
• If the ratio contains fractions, you must multiply all components by a factor to achieve a whole-number ratio (e.g., 6.5 : 1 : 9 becomes 13 : 2 : 18 when multiplied by 2).
• The instructor notes that the empirical formula is multiplied by an integer factor to get the molecular formula, which depends on the compound’s molar mass.
• The example discusses vanillin (a C, H, O-containing compound) and, in a combustion context, mentions ethanol as a comparison, illustrating the general applicability of the method to compounds containing C, H, and O.
• A key practical tip is to always write out the combustion reaction first to stay organized and to keep track of which atoms come from the compound versus from O₂.
• The transcript reinforces the concept of excess O₂ ensuring complete combustion and highlights that oxygen in the products partly derives from the added O₂ rather than exclusively from the sample.
• The process relies on basic chemical principles: the law of conservation of mass, the mole concept, and stoichiometry.
• Common pitfalls to watch for include fractional ratios, misordering of elements when reporting empirical formulas (C:H:O order), and not having enough information to perform mass-balance for O without a total sample mass.

Practical takeaways and tips

• Always label the reactants and products clearly and write the balanced (or at least the expected) combustion equation: hydrocarbon + O₂ → CO₂ + H₂O.
• Use CO₂ to deduce C content and H₂O to deduce H content; apply the factor of 2 for H in H₂O.
• Use mass balance to determine the oxygen content in the original sample when O₂ is in excess.
• When forming the empirical formula, ensure you present the ratio in C:H:O; clear any fractions by multiplying to obtain integers.
• To obtain the molecular formula, compute the empirical formula mass and compare with the actual molar mass; multiply the empirical formula by the resulting integer factor if needed.
• Keep track of units and significant figures; use the standard atomic masses: $M<em>C \approx 12.01\ \text{g/mol},\ M</em>H \approx 1.008\ \text{g/mol},\ M_O \approx 16.00\ \text{g/mol}.$