GATE 2024 MT – Question 58
A nonporous spherical Fe$_2$O$_3$ particle of initial radius $5\times10^{-2}$ m is topochemically reduced by H$_2$. The sharp reactant–product interface remains spherical, and rate is proportional to its area. The unreacted radius after 600 s is ______ $\times10^{-2}$ m (nearest integer). Given: $k=5\times10^{-5}$ m s$^{-1}$.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2 to 2
Explanation
Area-proportional reaction gives constant radial retreat speed, $-dr/dt=k$.
Integrating gives $r=r_0-kt$.
Thus $r=0.05-(5\times10^{-5})(600)=0.02$ m.
The requested coefficient is **2**.