Question

The ratio of the moles of CO$_2$ evolved to the moles of O$_2$ consumed in respiration, also called the respiratory quotient (RQ), is calculated for a carbohydrate (C$_6$H$_{12}$O$_6$) as substrate and found to be 1. Under similar conditions, for a fatty acid (C$_{51}$H$_{98}$O$_6$) as substrate, the respiratory quotient is ________________ (rounded off to two decimal places).

Hint:

- Carbohydrates: RQ = 1
- Fats: RQ<1 (generally 0.7–0.8)
- Proteins: RQ ≈ 0.8–0.9

Answer 1

Correct Answer: 0.65

Step 1: General formula for Respiratory Quotient (RQ).
\[ RQ = \frac{\text{moles of CO$_2$ produced}}{\text{moles of O$_2$ consumed}} \]
Step 2: Respiration equation for carbohydrate (glucose).
\[ C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O \] Here, CO$_2$ produced = 6, O$_2$ consumed = 6. \[ RQ = \frac{6}{6} = 1 \] This matches the given condition.
Step 3: Respiration equation for fatty acid (C$_{51}$H$_{98}$O$_6$).
The oxidation equation is: \[ C_{51}H_{98}O_6 + 72.5O_2 \rightarrow 51CO_2 + 49H_2O \]
Step 4: Calculate RQ.
\[ RQ = \frac{51}{72.5} \approx 0.703 \approx 0.71 \] Final Answer: \[ \boxed{0.71} \]