GATE 2022 BT Q.29: solution and answer

Official answer: 4Source: Official answer key, GATE 2022 BT (IIT Kharagpur)

1. The degree of reduction $\gamma$ is the number of available electrons per carbon atom (per C-mole). It is measured against ${\text{CO}}_2$, ${\text{H}}_2\text{O}$ and ${\text{NH}}_3$, which all count as zero. Each atom is assigned a valence: C = 4, H = 1, O = $-2$. For a compound ${\text{C}}_c{\text{H}}_h{\text{O}}_o$ with no nitrogen: $$\gamma =\frac{4c+h-2o}{c}$$

2. Lactic acid ${\text{C}}_3{\text{H}}_6{\text{O}}_3$ has $c=3$, $h=6$, $o=3$.

3. Available electrons per molecule: $4(3)+1(6)-2(3)=12+6-6=12$.

4. Divide by the number of carbons: $$\gamma =\frac{12}{3}=4$$

5. Check: per C-mole, lactic acid is ${\text{CH}}_2\text{O}$, the same as glucose (${\text{C}}_6{\text{H}}_{12}{\text{O}}_6\to {\text{CH}}_2\text{O}$), and glucose also has $\gamma =4$. That fits homolactic fermentation (glucose to 2 lactate), which is redox-balanced and needs no external electron acceptor.