GATE 2019 BT Q.23: solution and answer

Official answer: 4Source: Official answer key, GATE 2019 BT (IIT Madras)

1. The degree of reduction $\gamma$ is the number of available electrons per carbon atom (per C-mole). It is counted against the reference compounds ${\text{CO}}_2$, ${\text{H}}_2\text{O}$ and ${\text{NH}}_3$, which have $\gamma =0$. The valences used are C = +4, H = +1, O = −2 and N = −3.

2. For a compound ${\text{C}}_w{\text{H}}_x{\text{O}}_y{\text{N}}_z$: $$\gamma =\frac{4w+x-2y-3z}{w}$$

3. Acetic acid ${\text{C}}_2{\text{H}}_4{\text{O}}_2$ has $w=2$, $x=4$, $y=2$ and $z=0$.

4. Available electrons per molecule: $4(2)+4-2(2)-3(0)=8+4-4=8$.

5. Divide by the number of carbon atoms: $$\gamma =\frac{8}{2}=4$$

6. Check with the C-mole formula: ${\text{C}}_2{\text{H}}_4{\text{O}}_2$ divided by 2 gives ${\text{CH}}_2\text{O}$, so $\gamma =4+2-2(1)=4$. This is the same as glucose, whose C-mole formula is also ${\text{CH}}_2\text{O}$.