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Sagot :
Sure, let's balance these chemical equations step-by-step.
### i) [tex]\( \text{Al} + \text{HCl} \rightarrow \)[/tex]
The unbalanced equation is:
[tex]\[ \text{Al} + \text{HCl} \rightarrow \text{AlCl}_3 + \text{H}_2 \][/tex]
To balance this equation, we need to ensure that the number of atoms for each element is the same on both sides of the equation.
1. Balance Aluminum (Al):
There is 1 Al atom on the left and 1 Al atom on the right, so aluminum is balanced.
2. Balance Chlorine (Cl):
On the right side, there are 3 Cl atoms (in [tex]\(\text{AlCl}_3\)[/tex]). On the left, there is 1 Cl atom in each [tex]\(\text{HCl}\)[/tex]. Since we need 3 Cl atoms, we should have 3 [tex]\(\text{HCl}\)[/tex] molecules. However, the hydrogen atoms will then be unbalanced. To resolve this, we will use a multiple of 3, which makes it easier to balance the hydrogen atoms later. Let's try using 6 [tex]\(\text{HCl}\)[/tex] molecules:
[tex]\[ 6 \text{HCl} \][/tex]
3. Balance Hydrogen (H):
With 6 [tex]\(\text{HCl}\)[/tex] on the left side, we get:
[tex]\[ 2\text{Al} + 6\text{HCl} \rightarrow 2\text{AlCl}_3 + 3\text{H}_2 \][/tex]
- [tex]\( 6 \text{H}\)[/tex] atoms on the left side and [tex]\( 3 \cdot 2 = 6 \text{H}\)[/tex] atoms on the right side from [tex]\(3 \text{H}_2\)[/tex] molecules.
So, the balanced equation is:
[tex]\[ 2 \text{Al} + 6 \text{HCl} \rightarrow 2 \text{AlCl}_3 + 3 \text{H}_2 \][/tex]
### ii) [tex]\( \text{Mg} + \text{HNO}_3 \rightarrow \)[/tex]
The unbalanced equation is:
[tex]\[ \text{Mg} + \text{HNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + \text{H}_2 \][/tex]
To balance this equation, follow these steps:
1. Balance Magnesium (Mg):
There is 1 Mg atom on the left and 1 Mg atom on the right, so magnesium is balanced.
2. Balance Nitrate (NO[tex]\(_3\)[/tex]):
On the right side, there are 2 nitrate ([tex]\(\text{NO}_3\)[/tex]) groups in [tex]\(\text{Mg(NO}_3\text{)}_2\)[/tex]. On the left, there is 1 nitrate group in each [tex]\(\text{HNO}_3\)[/tex]. So, we need 2 [tex]\(\text{HNO}_3\)[/tex] molecules to balance the nitrate groups:
[tex]\[ 2 \text{HNO}_3 \][/tex]
3. Balance Hydrogen (H):
With 2 [tex]\(\text{HNO}_3\)[/tex] on the left side, we get:
[tex]\[ \text{Mg} + 2 \text{HNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + \text{H}_2 \][/tex]
- [tex]\( 2 \text{H}\)[/tex] atoms on the left side and [tex]\( 2 \text{H}\)[/tex] atoms on the right side from [tex]\( 1 \text{H}_2\)[/tex] molecule.
So, the balanced equation is:
[tex]\[ \text{Mg} + 2 \text{HNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + \text{H}_2 \][/tex]
In conclusion, the balanced equations are:
i) [tex]\( 2 \text{Al} + 6 \text{HCl} \rightarrow 2 \text{AlCl}_3 + 3 \text{H}_2 \)[/tex]
ii) [tex]\( \text{Mg} + 2 \text{HNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + \text{H}_2 \)[/tex]
### i) [tex]\( \text{Al} + \text{HCl} \rightarrow \)[/tex]
The unbalanced equation is:
[tex]\[ \text{Al} + \text{HCl} \rightarrow \text{AlCl}_3 + \text{H}_2 \][/tex]
To balance this equation, we need to ensure that the number of atoms for each element is the same on both sides of the equation.
1. Balance Aluminum (Al):
There is 1 Al atom on the left and 1 Al atom on the right, so aluminum is balanced.
2. Balance Chlorine (Cl):
On the right side, there are 3 Cl atoms (in [tex]\(\text{AlCl}_3\)[/tex]). On the left, there is 1 Cl atom in each [tex]\(\text{HCl}\)[/tex]. Since we need 3 Cl atoms, we should have 3 [tex]\(\text{HCl}\)[/tex] molecules. However, the hydrogen atoms will then be unbalanced. To resolve this, we will use a multiple of 3, which makes it easier to balance the hydrogen atoms later. Let's try using 6 [tex]\(\text{HCl}\)[/tex] molecules:
[tex]\[ 6 \text{HCl} \][/tex]
3. Balance Hydrogen (H):
With 6 [tex]\(\text{HCl}\)[/tex] on the left side, we get:
[tex]\[ 2\text{Al} + 6\text{HCl} \rightarrow 2\text{AlCl}_3 + 3\text{H}_2 \][/tex]
- [tex]\( 6 \text{H}\)[/tex] atoms on the left side and [tex]\( 3 \cdot 2 = 6 \text{H}\)[/tex] atoms on the right side from [tex]\(3 \text{H}_2\)[/tex] molecules.
So, the balanced equation is:
[tex]\[ 2 \text{Al} + 6 \text{HCl} \rightarrow 2 \text{AlCl}_3 + 3 \text{H}_2 \][/tex]
### ii) [tex]\( \text{Mg} + \text{HNO}_3 \rightarrow \)[/tex]
The unbalanced equation is:
[tex]\[ \text{Mg} + \text{HNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + \text{H}_2 \][/tex]
To balance this equation, follow these steps:
1. Balance Magnesium (Mg):
There is 1 Mg atom on the left and 1 Mg atom on the right, so magnesium is balanced.
2. Balance Nitrate (NO[tex]\(_3\)[/tex]):
On the right side, there are 2 nitrate ([tex]\(\text{NO}_3\)[/tex]) groups in [tex]\(\text{Mg(NO}_3\text{)}_2\)[/tex]. On the left, there is 1 nitrate group in each [tex]\(\text{HNO}_3\)[/tex]. So, we need 2 [tex]\(\text{HNO}_3\)[/tex] molecules to balance the nitrate groups:
[tex]\[ 2 \text{HNO}_3 \][/tex]
3. Balance Hydrogen (H):
With 2 [tex]\(\text{HNO}_3\)[/tex] on the left side, we get:
[tex]\[ \text{Mg} + 2 \text{HNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + \text{H}_2 \][/tex]
- [tex]\( 2 \text{H}\)[/tex] atoms on the left side and [tex]\( 2 \text{H}\)[/tex] atoms on the right side from [tex]\( 1 \text{H}_2\)[/tex] molecule.
So, the balanced equation is:
[tex]\[ \text{Mg} + 2 \text{HNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + \text{H}_2 \][/tex]
In conclusion, the balanced equations are:
i) [tex]\( 2 \text{Al} + 6 \text{HCl} \rightarrow 2 \text{AlCl}_3 + 3 \text{H}_2 \)[/tex]
ii) [tex]\( \text{Mg} + 2 \text{HNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + \text{H}_2 \)[/tex]
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