Sure, let's tackle each part of the question step-by-step.
### Part (i): Construct an Ionic Equation for the Reaction of Magnesium with an Acid
When magnesium reacts with hydrochloric acid (HCl) or ethanoic acid (CH₃COOH), it produces hydrogen gas (H₂) and a salt (MgCl₂ in the case of hydrochloric acid and Mg(CH₃COO)₂ in the case of ethanoic acid). The same ionic equation can describe both reactions since both acids provide [tex]\( \text{H}^+ \)[/tex] ions for the reaction.
The general ionic equation for the reaction of magnesium with an acid is:
[tex]\[ \text{Mg (s)} + 2 \text{H}^+ (\text{aq}) \rightarrow \text{Mg}^{2+} (\text{aq}) + \text{H}_2 (\text{g}) \][/tex]
### Part (ii): Explanation for Different Reaction Rates but Same Volume of Gas Produced
#### Why the Same Volume of Gas is Produced
Regardless of the type of acid used, both reactions start with the same number of moles of acid. Here's the calculation:
1. Volume of acid solution:
[tex]\[ 25.0 \, \text{cm}^3 = 0.025 \, \text{dm}^3 \][/tex]
2. Concentration of both acids:
[tex]\[ 0.500 \, \text{mol dm}^{-3} \][/tex]
3. Number of moles of [tex]\( \text{H}^+ \)[/tex] ions provided by the acid:
[tex]\[
\text{Number of moles} = \text{concentration} \times \text{volume} = 0.500 \, \text{mol dm}^{-3} \times 0.025 \, \text{dm}^3 = 0.0125 \, \text{mol}
\][/tex]
Both hydrochloric acid (HCl) and ethanoic acid (CH₃COOH) will provide the same number of [tex]\( \text{H}^+ \)[/tex] ions, leading to the generation of the same amount of [tex]\( \text{H}_2 \)[/tex] gas.
#### Why Rates are Different
The difference in reaction rate can be explained by the strength of the acids:
1. Hydrochloric acid (HCl) is a strong acid:
- It fully dissociates in water, releasing all its [tex]\( \text{H}^+ \)[/tex] ions immediately.
[tex]\[
\text{HCl (aq)} \rightarrow \text{H}^+ (\text{aq}) + \text{Cl}^- (\text{aq})
\][/tex]
- This leads to a high concentration of [tex]\( \text{H}^+ \)[/tex] ions in the solution right from the start, resulting in a faster reaction rate with magnesium.
2. Ethanoic acid (CH₃COOH) is a weak acid:
- It partially dissociates in water, meaning that fewer [tex]\( \text{H}^+ \)[/tex] ions are available in the solution at any given time.
[tex]\[
\text{CH}_3\text{COOH (aq)} \rightleftharpoons \text{CH}_3\text{COO}^- (\text{aq}) + \text{H}^+ (\text{aq})
\][/tex]
- This lower concentration of [tex]\( \text{H}^+ \)[/tex] ions results in a slower reaction rate with magnesium.
In summary: Both reactions produce the same volume of gas because the moles of acid and hence [tex]\( \text{H}^+ \)[/tex] ions are the same for both acids. However, the reaction rates differ due to the differences in dissociation extent between the strong hydrochloric acid and the weak ethanoic acid.
