To determine the form of magnesium ([tex]\(Mg\)[/tex]) that will allow the reaction to occur at the fastest rate when added to water, we must consider the concept of surface area. The rate of a chemical reaction depends on the surface area of the reactants available to interact with each other.
In this reaction:
[tex]\[
Mg (s) + 2 H_2O (\ell) \rightarrow Mg(OH)_2 (s) + H_2 (g)
\][/tex]
the magnesium and water must come into contact with each other for the reaction to proceed. Therefore, the more surface area of the magnesium that is exposed to the water, the faster the reaction will occur.
Let's look at the different forms of magnesium presented in the options:
1. Large chunks:
- Large chunks of magnesium have a relatively small surface area exposed to the water compared to their volume. Thus, the reaction would proceed more slowly.
2. Small chunks:
- Small chunks have a larger total surface area exposed to the water compared to large chunks, so the reaction would be faster than with large chunks, but still not optimal.
3. A ribbon:
- A ribbon of magnesium would have a long, narrow shape, increasing the surface area compared to large chunks. This would allow the reaction to proceed more quickly than with large chunks or small chunks, but it still isn't the form with the most surface area.
4. A powder:
- A powder consists of very fine particles, each with a significant surface area exposed to the water. This maximizes the contact between magnesium and water, thus allowing the reaction to proceed at the fastest rate.
Considering all these points, the form of [tex]\(1 \, g\)[/tex] of [tex]\(Mg (s)\)[/tex] that should be added to the water for the fastest reaction rate is:
(4) a powder
