Understanding Respiratory Quotient (RQ)

The Respiratory Quotient (RQ) is a measure used in cellular respiration. It is defined as the ratio of the volume of carbon dioxide ($CO_2$) produced to the volume of oxygen ($O_2$) consumed during the process.

The formula for RQ is:

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

RQ Calculation for the Given Biomolecule

The provided equation is:

$ 2(C_{51}H_{98}O_{6}) + 145O_{2} \rightarrow 102CO_{2} + 98H_{2}O + \text{energy} $

From this balanced equation, we can identify the volumes (or moles) of $CO_2$ produced and $O_2$ consumed:

• Volume of $CO_2$ produced = 102
• Volume of $O_2$ consumed = 145

Now, we calculate the RQ using the formula:

$ RQ = \frac{102}{145} $

$ RQ \approx 0.703 $

Determining the Biomolecule Type and RQ Range

The molecule $C_{51}H_{98}O_{6}$ is a representation of a fat or lipid. Fats are characterized by a lower proportion of oxygen compared to carbohydrates.

• Carbohydrates typically yield an RQ of 1.
• Fats yield an RQ less than 1, usually between 0.5 and 0.95, because they require more oxygen for complete oxidation and produce less $CO_2$ relative to oxygen consumed.
• Proteins yield an RQ around 0.8 to 0.9.

Our calculated RQ of approximately 0.703 falls within the typical range for fats.

Conclusion on RQ Value

The calculated RQ of approximately 0.703 indicates that the biomolecule undergoing respiration is likely a fat. Therefore, the RQ falls within the range of 0.5 to 0.95.