Q.A zero order reaction is 20% complete in 20 minutes. Calculate the value of the rate constant. In what time will the reaction be 80% complete?

Step 1. For a zero order reaction, the fraction reacted x (as a fraction of $[A]_0$) satisfies $x\,[A]_0=kt$, i.e. $k=\dfrac{x[A]_0}{t}$.

Step 2. At 20% complete ($x=0.20$) in $t=20$ min: $k=\dfrac{0.20\times[A]_0}{20}=0.01\times[A]_0\ \text{mol L}^{-1}\text{min}^{-1}$ -- since no numerical initial concentration is given in this question, k can only be expressed IN TERMS OF $[A]_0$, not as a bare number (an honest gap: quoting a specific number for k here without a stated $[A]_0$ would be a fabrication).

Step 3. For the SECOND part, the ratio $k/[A]_0=0.01\ \text{min}^{-1}$ is fixed regardless of the unknown $[A]_0$, since $[A]_0$ cancels: $x=(k/[A]_0)\times t$. …

Express the fraction reacted for a zero order reaction as $x[A]_0=kt$; since no absolute initial concentration is stated, express k proportionally, but note that the SECOND p …

• Assuming $[A]_0=1$ M silently to force out a bare numeric value for k, when the question genuinely never states an initial concentration -- honest practice is to express k in terms of $[A]_0$ rather than inventing a number. …