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Q10:
Define RQ. What is its value for fats?

Solution :

1. Definition of Respiratory Quotient (RQ)

The Respiratory Quotient (RQ), also known as the Respiratory Ratio, is a dimensionless unit used in respiratory physiology to calculate which fuel (carbohydrate, fat, or protein) is being metabolized by an organism. It is defined as the ratio of the volume of carbon dioxide ($CO_2$) evolved to the volume of oxygen ($O_2$) consumed during the process of aerobic respiration.

The mathematical representation is given by the formula:

$RQ = \frac{\text{Volume of } CO_2 \text{ evolved}}{\text{Volume of } O_2 \text{ consumed}}$

2. Respiratory Quotient for Fats

When fats (lipids) serve as the respiratory substrate, they must first be converted into smaller molecules before entering the Krebs cycle. Because fats are more reduced than carbohydrates, they require significantly more oxygen for complete oxidation [Per the stoichiometry of fatty acid oxidation].

3. Derivation and Calculation

Consider the complete oxidation of Tripalmitin, a common fatty acid (fat), as a representative reaction:

$2(C_{51}H_{98}O_6) + 145 O_2 \rightarrow 102 CO_2 + 98 H_2O + \text{Energy}$

Applying the RQ formula to this reaction:

$RQ = \frac{102 \text{ molecules of } CO_2}{145 \text{ molecules of } O_2}$

$RQ \approx 0.7$

4. Visualization of Metabolic Gas Exchange

Fat Input Resulting Gas $O_2$ consumed (145) $CO_2$ evolved (102) RQ = 102 / 145 = 0.7

5. Analytical Conclusion

The value of the Respiratory Quotient is generally less than unity ($RQ < 1.0$) for fats. This signifies that the organism is consuming a greater volume of oxygen than the volume of carbon dioxide it is releasing, a direct consequence of the higher hydrogen-to-carbon ratio in lipid molecules compared to glucose [Based on biochemical energy density and oxidation stoichiometry].

Final Solution: The Respiratory Quotient (RQ) for fats is approximately 0.7.


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