calculate RQ values of different respiratory substrates from equations for respiration

Published by Patrick Mutisya · 14 days ago

Cambridge A-Level Biology 9700 – Energy: Calculating Respiratory Quotient (RQ)

Energy – Respiratory Quotient (RQ)

The respiratory quotient (RQ) is the ratio of carbon dioxide produced to oxygen consumed during cellular respiration:

\$\text{RQ} = \frac{\text{CO}2\text{ produced}}{\text{O}2\text{ consumed}}\$

Different respiratory substrates (carbohydrates, fats, proteins) yield different RQ values because their oxidation reactions consume different amounts of O₂ relative to the CO₂ generated.

Why RQ is important

  • Indicates which substrate is being metabolised.

  • Helps interpret indirect calorimetry data.

  • Useful in clinical nutrition and exercise physiology.

General approach to calculate RQ

  1. Write the balanced aerobic oxidation equation for the substrate.

  2. Identify the number of moles of CO₂ produced (numerator).

  3. Identify the number of moles of O₂ consumed (denominator).

  4. Divide CO₂ moles by O₂ moles to obtain RQ.

Typical respiratory substrates

SubstrateBalanced oxidation equationCO₂ produced (mol)O₂ consumed (mol)RQ value
Glucose (carbohydrate)\$\mathrm{C6H{12}O6 + 6\,O2 \rightarrow 6\,CO2 + 6\,H2O}\$661.00
Palmitic acid (fatty acid, C₁₆)\$\mathrm{C{16}H{32}O2 + 23\,O2 \rightarrow 16\,CO2 + 16\,H2O}\$16230.70
Alanine (representative amino acid)\$\mathrm{C3H7NO2 + 2.5\,O2 \rightarrow 3\,CO2 + 2.5\,H2O + NH_3}\$32.51.20
Mixed diet (average)— (average of multiple substrates) —≈ 0.85 × O₂ consumed—≈ 0.85

Step‑by‑step example: Calculating RQ for palmitic acid

1. Write the oxidation equation (shown in the table):

\$\mathrm{C{16}H{32}O2 + 23\,O2 \rightarrow 16\,CO2 + 16\,H2O}\$

2. Identify moles of CO₂ produced = 16 mol.

3. Identify moles of O₂ consumed = 23 mol.

4. Apply the RQ formula:

\$\text{RQ} = \frac{16}{23} \approx 0.70\$

Key points to remember

  • Carbohydrates give an RQ of \overline{1}.0 because each C atom is fully oxidised to CO₂ with a 1:1 O₂:CO₂ ratio.

  • Fats give a lower RQ (\overline{0}.7) because they contain more reduced carbon (more H relative to O) and require more O₂ per CO₂ produced.

  • Proteins give an RQ >1 (typically 0.8–1.0 for whole‑protein mixtures) because deamination releases nitrogen and additional CO₂ is produced from the carbon skeleton.

  • Mixed diets produce intermediate RQ values (≈0.85), reflecting the proportion of each substrate being oxidised.

Suggested diagram: A bar chart comparing RQ values for glucose, palmitic acid, and alanine.

Practice question

Calculate the RQ for the oxidation of the carbohydrate fructose, whose empirical formula is \$\mathrm{C6H{12}O_6}\$ (same as glucose). Show all steps.

Answer outline

  1. Write the balanced equation: \$\mathrm{C6H{12}O6 + 6\,O2 \rightarrow 6\,CO2 + 6\,H2O}\$

  2. CO₂ produced = 6 mol; O₂ consumed = 6 mol.

  3. RQ = \$6/6 = 1.00\$.