calculate RQ values of different respiratory substrates from equations for respiration

Energy – Respiratory Quotient (RQ)

What is RQ? (AO1)

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

\[ \text{RQ} = \frac{\text{moles of CO}_2\text{ produced}}{\text{moles of O}_2\text{ consumed}} \] It is a dimension‑less number that reveals which class of substrate (carbohydrate, lipid or protein) is being oxidised.

Why RQ matters in A‑Level Biology (AO1, AO2, AO3)

• Identifies the predominant respiratory substrate in a physiological or experimental situation.
• Enables interpretation of indirect calorimetry data (exercise physiology, clinical nutrition).
• Links substrate utilisation to ATP yield – a lower RQ generally means more ATP per mole of O₂ used (fat oxidation).

General method for calculating RQ (AO2)

1. Write the balanced aerobic oxidation equation for the substrate.
2. Read the stoichiometric coefficient of CO₂ (numerator).
3. Read the stoichiometric coefficient of O₂ (denominator).
4. Divide CO₂ mol by O₂ mol and simplify.

Balanced oxidation equations (AO1)

Substrate type	Representative molecule	Balanced aerobic oxidation equation	CO₂ (mol)	O₂ (mol)	RQ
Carbohydrate	Glucose (C₆H₁₂O₆)	\(\mathrm{C_6H_{12}O_6 + 6\,O_2 \rightarrow 6\,CO_2 + 6\,H_2O}\)	6	6	1.00
Lipid (fatty acid)	Palmitic acid (C₁₆H₃₂O₂)	\(\mathrm{C_{16}H_{32}O_{2} + 23\,O_2 \rightarrow 16\,CO_2 + 16\,H_2O}\)	16	23	0.70
Protein (average whole‑protein mixture)	Alanine (C₃H₇NO₂) – illustrative	\(\mathrm{C_3H_7NO_2 + 2.5\,O_2 \rightarrow 3\,CO_2 + 2.5\,H_2O + NH_3}\)	3	2.5	1.20\;(\text{single amino‑acid only})
Mixed diet (average of carbs, fats & proteins)	—	—	≈ 0.85 × O₂ consumed	—	≈ 0.85

Note: Whole‑protein oxidation does not give a single RQ; the value depends on how nitrogen is excreted. In humans most nitrogen leaves as urea, giving an overall protein RQ of ~0.80–0.90, whereas in many laboratory animals ammonia excretion pushes the value slightly higher.

Worked examples (AO2)

1. RQ for palmitic acid

1. Equation: \(\mathrm{C_{16}H_{32}O_{2} + 23\,O_2 \rightarrow 16\,CO_2 + 16\,H_2O}\)
2. CO₂ = 16 mol, O₂ = 23 mol
3. \(\displaystyle \text{RQ}= \frac{16}{23}=0.70\) (2 dp)

2. RQ for oleic acid (C₁₈H₃₄O₂)

\[ \mathrm{C_{18}H_{34}O_{2} + 25.5\,O_2 \rightarrow 18\,CO_2 + 17\,H_2O} \] \[ \text{RQ}= \frac{18}{25.5}=0.71 \]

3. Converting gas volumes to moles (ideal‑gas example)

In a respirometer the following changes are recorded after 10 min at 298 K and 1 atm:

• ΔV_O₂ = 0.025 L (decrease)
• ΔV_CO₂ = 0.020 L (increase, after CO₂ is not absorbed)

Using the ideal‑gas equation \(PV = nRT\) (R = 0.0821 L·atm·K⁻¹·mol⁻¹):

\[ n_{\mathrm{O_2}} = \frac{P\,V}{R\,T}= \frac{1.00\;\text{atm}\times0.025\;\text{L}}{0.0821\;\text{L·atm·K}^{-1}\text{mol}^{-1}\times298\;\text{K}} = 1.02\times10^{-3}\;\text{mol} \] \[ n_{\mathrm{CO_2}} = \frac{1.00\times0.020}{0.0821\times298}=8.15\times10^{-4}\;\text{mol} \] \[ \text{RQ}= \frac{8.15\times10^{-4}}{1.02\times10^{-3}}=0.80\;(2\;\text{dp}) \]

The experimental RQ of 0.80 suggests a mixed utilisation of carbohydrate and fat.

Link between RQ and ATP yield (AO3)

• Glucose → ≈ 30 ATP per molecule; RQ = 1.00.
• Palmitic acid → ≈ 106 ATP per molecule; RQ ≈ 0.70 (more O₂ required per CO₂, so more ATP per O₂).
• Protein (average) → ≈ 21 ATP per amino‑acid residue after deamination; RQ ≈ 0.80‑0.90.

Thus a lower RQ generally indicates a substrate that yields more ATP per mole of O₂, which explains why fat oxidation predominates during prolonged, low‑intensity exercise.

Practical investigation: Determining RQ with a simple respirometer (AO4)

1. Place 5 g of germinating beans in a sealed syringe‑type respirometer containing a known volume of air (≈ 30 mL).
2. Connect one outlet to a soda‑lime tube (absorbs CO₂) and the other to a water‑filled graduated tube to record volume changes.
3. Incubate at a constant temperature (e.g. 25 °C) for a fixed period (10 min).
4. Read the decrease in O₂ volume (ΔV_O₂) and the increase in CO₂ volume (ΔV_CO₂) after the period.
5. Convert each volume to moles using \(n = PV/RT\) (show all substitutions).
6. Calculate RQ = n_CO₂ / n_O₂.

Sample calculation (using the data from the ideal‑gas example above)

5. For O₂: \(n = \dfrac{1.00\times0.025}{0.0821\times298}=1.02\times10^{-3}\;\text{mol}\)
6. For CO₂: \(n = \dfrac{1.00\times0.020}{0.0821\times298}=8.15\times10^{-4}\;\text{mol}\)
7. RQ = \(8.15\times10^{-4}/1.02\times10^{-3}=0.80\)

Error‑analysis table (AO4)

Potential source of error	Effect on measured ΔVO₂ or ΔVCO₂	Resulting bias in RQ
Leakage of the respirometer	Both O₂ loss and CO₂ escape are underestimated.	RQ may be either higher or lower depending on which gas leaks more.
Incomplete CO₂ absorption by soda‑lime	ΔVCO₂ appears larger than true.	RQ is over‑estimated (suggests more carbohydrate).
Temperature drift (affects gas volume)	Volumes recorded at a temperature different from the one used in the PV = nRT calculation.	Systematic error in both n values → RQ may be inaccurate.
Calibration error of the graduated tube	Systematic over‑ or under‑reading of volumes.	Bias proportional to the direction of mis‑calibration.

Mixed‑diet RQ calculation (AO2)

If a diet supplies 60 % carbohydrate, 30 % fat and 10 % protein (by oxidised energy), the overall RQ is the weighted average of the individual RQs:

\[ \text{RQ}_{\text{mix}} = 0.60(1.00) + 0.30(0.70) + 0.10(0.85) \approx 0.85 \]

This matches the “average” value quoted for a typical human mixed diet.

Key points to remember (AO1)

• Carbohydrates give RQ = 1.00 (1 mol CO₂ per 1 mol O₂).
• Fats give a lower RQ (≈ 0.70) because they contain more reduced carbon and need more O₂ per CO₂.
• Protein RQ is not fixed; whole‑protein mixtures give ≈ 0.80‑0.90, influenced by nitrogen excretion (urea vs. ammonia).
• Mixed diets yield an intermediate RQ (~0.85), reflecting the proportion of each substrate.
• RQ is linked to ATP yield – lower RQ → more ATP per mole of O₂.

Practice questions

1. Fructose has the same empirical formula as glucose (C₆H₁₂O₆). Calculate its RQ.
   Answer: 1.00 (same balanced equation as glucose).
2. Oxidation of oleic acid (C₁₈H₃₄O₂): \(\mathrm{C_{18}H_{34}O_{2} + 25.5\,O_{2} \rightarrow 18\,CO_{2} + 17\,H_{2}O}\). Determine the RQ.
   Solution: RQ = 18 / 25.5 ≈ 0.71.
3. In a respirometer experiment, 0.030 mol O₂ are consumed and 0.025 mol CO₂ are produced. What substrate(s) are most likely being oxidised?
   Hint: Experimental RQ = 0.83 – compare with textbook values (carb = 1.00, fat ≈ 0.70, protein ≈ 0.80‑0.90).
   Answer: Predominantly a mixed utilisation of carbohydrate and fat, with a small protein contribution.

Assessment Objective (AO) alignment

• AO1 – Knowledge: Define RQ, list typical RQ values (quick‑reference box), write balanced oxidation equations for carbohydrate, lipid, protein (including note on variability) and mixed diet.
• AO2 – Application: Calculate RQ from given equations, perform unit‑conversion using the ideal‑gas law, compute mixed‑diet RQ, interpret respirometer data.
• AO3 – Analysis: Explain why different substrates give different RQ values and relate RQ to ATP yield per mole of O₂.
• AO4 – Evaluation: Design a simple experiment to measure RQ, show a full worked calculation, and evaluate sources of error (error‑analysis table).