A solid catalyst is finely divided to increase its surface area. If a total surface area of is requi — Surface Chemistry Chemistry Question
Question
A solid catalyst is finely divided to increase its surface area. If a total surface area of $6291456 \text{ cm}^2$ is required for a gaseous reaction, how many sequential splits must be made to a solid cube of exactly $1 \text{ cm}$ length to achieve this? (Assume 1 split yields 8 equal cubes).
Answer: C
💡 Solution & Explanation
The surface area of a cube after $n$ splits ($8^n$ total cubes) is given by $6 \times 2^n$. Equating $6 \times 2^n = 6291456$, we get $2^n = 1048576$. Since $2^{20} = 1048576$, exactly 20 splits are required.
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