若知道鋅與鹽酸之反應速率常數為 2.4×10-2 （M-1•min-l）。今將每邊長為8公分之正立方體鋅塊與足量之1M之鹽酸反應，其反應速率為S，再將該鋅塊切成每邊長 2公分之小正立方體，與濃度 0.25 M之足量鹽酸反應，試問反應速率變為多少？

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∻Solution∻ ‖ 1 ⋮ **Identify the initial conditions**: The initial reaction involves a zinc cube with a side length of 8 cm reacting with $1 \, ext{M}$ hydrochloric acid. The reaction rate constant is given as $2.4 imes 10^{-2} \, ext{M}^{-1} \cdot ext{min}^{-1}$. ‖ ‖ 2 ⋮ **Calculate the surface area of the initial zinc cube**: The surface area of a cube with side length 8 cm is $6 imes (8 \, ext{cm})^2 = 384 \, ext{cm}^2$. ‖ ‖ 3 ⋮ **Calculate the surface area of the smaller zinc cubes**: When the zinc cube is cut into smaller cubes with side length 2 cm, the number of smaller cubes is $(8/2)^3 = 64$. The surface area of each smaller cube is $6 imes (2 \, ext{cm})^2 = 24 \, ext{cm}^2$. Therefore, the total surface area of the smaller cubes is $64 imes 24 \, ext{cm}^2 = 1536 \, ext{cm}^2$. ‖ ‖ 4 ⋮ **Determine the new reaction rate**: The reaction rate is proportional to the surface area and the concentration of hydrochloric acid. The initial reaction rate $S$ is proportional to $384 \, ext{cm}^2 imes 1 \, ext{M}$. The new reaction rate $S'$ is proportional to $1536 \, ext{cm}^2 imes 0.25 \, ext{M}$. Therefore, $S' = S imes \frac{1536 \, ext{cm}^2 imes 0.25 \, ext{M}}{384 \, ext{cm}^2 imes 1 \, ext{M}} = S imes 1 = S$. ‖ ∻Answer∻ ⚹ The reaction rate remains the same, $S$. ⚹ ∻Key Concept∻ ⚹ Surface area and concentration affect reaction rates ⚹ ∻Explanation∻ ⚹ The reaction rate is directly proportional to the surface area of the reactant and the concentration of the reactant in solution. In this case, the increase in surface area is exactly balanced by the decrease in concentration, resulting in no change in the overall reaction rate. ⚹◊What is the rate law expression for the reaction between zinc and hydrochloric acid in the presence of water⍭ Generate me a similar question◊

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