Understanding the Respiratory Quotient (RQ)

The respiratory quotient (RQ) is a ratio used in cellular respiration. It is defined as the ratio of the volume of carbon dioxide ($\text{CO}_2$) produced to the volume of oxygen ($\text{O}_2$) consumed during respiration.

Mathematically, the RQ is represented as:

$$ \text{RQ} = \frac{\text{Volume of } \text{CO}_2 \text{ produced}}{\text{Volume of } \text{O}_2 \text{ consumed}} $$

The value of the respiratory quotient depends on the type of respiratory substrate being oxidized.

Respiratory Quotient for Different Substrates

Let's look at the typical RQ values for common respiratory substrates:

• Carbohydrates: Carbohydrates, like glucose ($\text{C}_6\text{H}_{12}\text{O}_6$), are fully oxidized and the volume of $\text{CO}_2$ produced is equal to the volume of $\text{O}_2$ consumed. For glucose: $$ \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} $$ The RQ for carbohydrates is $\frac{6}{6} = 1$.
• Fats: Fats require more oxygen for complete oxidation compared to the amount of $\text{CO}_2$ produced because they contain less oxygen relative to carbon and hydrogen. For example, Tripalmitin ($\text{C}_{51}\text{H}_{98}\text{O}_6$): $$ 2\text{C}_{51}\text{H}_{98}\text{O}_6 + 145\text{O}_2 \rightarrow 102\text{CO}_2 + 98\text{H}_2\text{O} $$ The RQ for this fat is $\frac{102}{145} \approx 0.7$. The RQ for fats is generally less than 1.
• Proteins: Proteins also require more oxygen for complete oxidation compared to the $\text{CO}_2$ produced, similar to fats, but the value is typically higher than fats. The RQ for proteins is approximately 0.8 to 0.9. This value is also less than 1.
• Organic Acids: Organic acids contain more oxygen atoms relative to carbon and hydrogen compared to carbohydrates, fats, and proteins. This means less external oxygen is required for their oxidation. For example, Oxalic acid ($\text{C}_2\text{H}_2\text{O}_4$): $$ \text{C}_2\text{H}_2\text{O}_4 + 0.5\text{O}_2 \rightarrow 2\text{CO}_2 + \text{H}_2\text{O} $$ The RQ for Oxalic acid is $\frac{2}{0.5} = 4$. The RQ for organic acids is typically greater than 1.

Identifying Substances with Respiratory Quotient Less Than One

Based on the typical values:

• Fats have an RQ less than one ($\approx 0.7$).
• Proteins have an RQ less than one ($\approx 0.8-0.9$).
• Organic acids have an RQ greater than one (e.g., 4 for oxalic acid).

The question asks for the substance(s) where the respiratory quotient is less than one. Both fats and proteins fit this description.

Analyzing the Options

• Option 1: fats - RQ is less than one.
• Option 2: organic acids - RQ is greater than one.
• Option 3: proteins - RQ is less than one.
• Option 4: More than one of the above - Since both fats and proteins have an RQ less than one, this option is consistent with our understanding.
• Option 5: None of the above - This is incorrect as both fats and proteins have an RQ less than one.

Therefore, fats and proteins are substances where the respiratory quotient is less than one.