To balance the chemical equation [tex]\( \text{Cl}_2 + \text{KI} \rightarrow \text{KCl} + \text{I}_2 \)[/tex], we need to follow these steps to ensure that the same number of each type of atom appears on both sides of the reaction.
1. Identify the number of each type of atom on both sides of the equation:
- Left side:
- [tex]\(\text{Cl}_2\)[/tex]: 2 chlorine (Cl) atoms
- [tex]\(\text{KI}\)[/tex]: 1 potassium (K) atom and 1 iodine (I) atom
- Right side:
- [tex]\(\text{KCl}\)[/tex]: 1 potassium (K) atom and 1 chlorine (Cl) atom
- [tex]\(\text{I}_2\)[/tex]: 2 iodine (I) atoms
2. Balance one type of atom at a time:
- Let's start with iodine (I). On the right side, we have 2 iodine atoms in [tex]\(\text{I}_2\)[/tex], but on the left side, there is only 1 iodine atom in [tex]\(\text{KI}\)[/tex]. To balance the iodine atoms, we need to have 2 iodine atoms on the left side. Therefore, we need 2 [tex]\(\text{KI}\)[/tex]:
[tex]\[ \text{Cl}_2 + 2 \, \text{KI} \rightarrow \text{KCl} + \text{I}_2 \][/tex]
3. Reevaluate all atoms after the adjustment:
- Left side:
- [tex]\(\text{Cl}_2\)[/tex]: 2 chlorine (Cl) atoms
- [tex]\(2 \, \text{KI}\)[/tex]: 2 potassium (K) atoms and 2 iodine (I) atoms
- Right side:
- [tex]\(\text{KCl}\)[/tex]: 1 potassium (K) atom and 1 chlorine (Cl) atom
- [tex]\(\text{I}_2\)[/tex]: 2 iodine (I) atoms
4. Balance the chlorine (Cl) atoms:
- After adding the coefficient 2 in front of [tex]\(\text{KI}\)[/tex], there are now 2 potassium atoms and 2 iodine atoms on both sides. Looking at chlorine, the left side has 2 chlorine atoms from [tex]\(\text{Cl}_2\)[/tex].
- We need to balance the chlorine atoms by having 2 [tex]\(\text{KCl}\)[/tex] on the right:
[tex]\[ \text{Cl}_2 + 2 \, \text{KI} \rightarrow 2 \, \text{KCl} + \text{I}_2 \][/tex]
5. Final check:
- Left side:
- [tex]\(\text{Cl}_2\)[/tex]: 2 chlorine (Cl) atoms
- [tex]\(2 \, \text{KI}\)[/tex]: 2 potassium (K) atoms and 2 iodine (I) atoms
- Right side:
- [tex]\(2 \, \text{KCl}\)[/tex]: 2 potassium (K) atoms and 2 chlorine (Cl) atoms
- [tex]\(\text{I}_2\)[/tex]: 2 iodine (I) atoms
Each type of atom is now balanced on both sides of the equation. Therefore, we only needed to adjust the coefficient in front of [tex]\(\text{KI}\)[/tex] to 2 to balance the equation.
Thus, the balanced equation is:
[tex]\[ \text{Cl}_2 + 2 \, \text{KI} \rightarrow 2 \, \text{KCl} + \text{I}_2 \][/tex]
From the options provided, the correct answer is:
[tex]\[ \text{C. } 2 \, \text{KI} \][/tex]
