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Sagot :
To solve for the balanced coefficients in the chemical reaction, we need to balance each element on both sides of the equation. The unbalanced chemical reaction is:
[tex]\[ \text{SiCl}_4 + \text{H}_2\text{O} \rightarrow \text{SiO}_2 + \text{HCl} \][/tex]
We'll follow these steps:
1. Write down the number of atoms for each element in the reactants and products:
- Reactants:
- [tex]\( \text{SiCl}_4 \)[/tex]: 1 Si, 4 Cl
- [tex]\( \text{H}_2\text{O} \)[/tex]: 2 H, 1 O
- Products:
- [tex]\( \text{SiO}_2 \)[/tex]: 1 Si, 2 O
- [tex]\( \text{HCl} \)[/tex]: 1 H, 1 Cl
2. Set up the initial equation with coefficients:
Let's use variables [tex]\( a \)[/tex], [tex]\( b \)[/tex], [tex]\( c \)[/tex], and [tex]\( d \)[/tex] for the coefficients of [tex]\(\text{SiCl}_4\)[/tex], [tex]\(\text{H}_2\text{O}\)[/tex], [tex]\(\text{SiO}_2\)[/tex], and [tex]\(\text{HCl}\)[/tex], respectively. This gives us the equation:
[tex]\[ a \text{SiCl}_4 + b \text{H}_2\text{O} \rightarrow c \text{SiO}_2 + d \text{HCl} \][/tex]
3. Create and balance the equations for each element:
- Silicon (Si):
[tex]\[ a = c \][/tex]
- Chlorine (Cl):
[tex]\[ 4a = d \][/tex]
- Hydrogen (H):
[tex]\[ 2b = d \][/tex]
- Oxygen (O):
[tex]\[ b = 2c \][/tex]
4. Solve the system of equations:
From the silicon balance:
[tex]\[ a = c \][/tex]
From the chlorine balance:
[tex]\[ 4a = d \][/tex]
From the hydrogen balance:
[tex]\[ 2b = d \][/tex]
From the oxygen balance:
[tex]\[ b = 2a \][/tex]
Let's assign [tex]\( a = 1 \)[/tex]:
- From [tex]\( a = c \)[/tex]:
[tex]\[ c = 1 \][/tex]
- From [tex]\( 4a = d \)[/tex]:
[tex]\[ d = 4 \][/tex]
- From [tex]\( b = 2a \)[/tex]:
[tex]\[ b = 2 \][/tex]
5. Check the balanced reaction:
Substitute [tex]\( a = 1 \)[/tex], [tex]\( b = 2 \)[/tex], [tex]\( c = 1 \)[/tex], [tex]\( d = 4 \)[/tex] back into the reaction:
[tex]\[ 1 \text{SiCl}_4 + 2 \text{H}_2\text{O} \rightarrow 1 \text{SiO}_2 + 4 \text{HCl} \][/tex]
- Check silicon: 1 Si (left), 1 Si (right), balanced.
- Check chlorine: 4 Cl (left), 4 Cl (right), balanced.
- Check hydrogen: 4 H (left), 4 H (right), balanced.
- Check oxygen: 2 O (left), 2 O (right), balanced.
All elements are balanced, so the balanced equation is correct.
6. Sum of the coefficients:
Sum the coefficients:
[tex]\[ 1 (SiCl_4) + 2 (H_2O) + 1 (SiO_2) + 4 (HCl) = 8 \][/tex]
Therefore, the sum of the balanced coefficients is:
[tex]\[ \boxed{8} \][/tex]
[tex]\[ \text{SiCl}_4 + \text{H}_2\text{O} \rightarrow \text{SiO}_2 + \text{HCl} \][/tex]
We'll follow these steps:
1. Write down the number of atoms for each element in the reactants and products:
- Reactants:
- [tex]\( \text{SiCl}_4 \)[/tex]: 1 Si, 4 Cl
- [tex]\( \text{H}_2\text{O} \)[/tex]: 2 H, 1 O
- Products:
- [tex]\( \text{SiO}_2 \)[/tex]: 1 Si, 2 O
- [tex]\( \text{HCl} \)[/tex]: 1 H, 1 Cl
2. Set up the initial equation with coefficients:
Let's use variables [tex]\( a \)[/tex], [tex]\( b \)[/tex], [tex]\( c \)[/tex], and [tex]\( d \)[/tex] for the coefficients of [tex]\(\text{SiCl}_4\)[/tex], [tex]\(\text{H}_2\text{O}\)[/tex], [tex]\(\text{SiO}_2\)[/tex], and [tex]\(\text{HCl}\)[/tex], respectively. This gives us the equation:
[tex]\[ a \text{SiCl}_4 + b \text{H}_2\text{O} \rightarrow c \text{SiO}_2 + d \text{HCl} \][/tex]
3. Create and balance the equations for each element:
- Silicon (Si):
[tex]\[ a = c \][/tex]
- Chlorine (Cl):
[tex]\[ 4a = d \][/tex]
- Hydrogen (H):
[tex]\[ 2b = d \][/tex]
- Oxygen (O):
[tex]\[ b = 2c \][/tex]
4. Solve the system of equations:
From the silicon balance:
[tex]\[ a = c \][/tex]
From the chlorine balance:
[tex]\[ 4a = d \][/tex]
From the hydrogen balance:
[tex]\[ 2b = d \][/tex]
From the oxygen balance:
[tex]\[ b = 2a \][/tex]
Let's assign [tex]\( a = 1 \)[/tex]:
- From [tex]\( a = c \)[/tex]:
[tex]\[ c = 1 \][/tex]
- From [tex]\( 4a = d \)[/tex]:
[tex]\[ d = 4 \][/tex]
- From [tex]\( b = 2a \)[/tex]:
[tex]\[ b = 2 \][/tex]
5. Check the balanced reaction:
Substitute [tex]\( a = 1 \)[/tex], [tex]\( b = 2 \)[/tex], [tex]\( c = 1 \)[/tex], [tex]\( d = 4 \)[/tex] back into the reaction:
[tex]\[ 1 \text{SiCl}_4 + 2 \text{H}_2\text{O} \rightarrow 1 \text{SiO}_2 + 4 \text{HCl} \][/tex]
- Check silicon: 1 Si (left), 1 Si (right), balanced.
- Check chlorine: 4 Cl (left), 4 Cl (right), balanced.
- Check hydrogen: 4 H (left), 4 H (right), balanced.
- Check oxygen: 2 O (left), 2 O (right), balanced.
All elements are balanced, so the balanced equation is correct.
6. Sum of the coefficients:
Sum the coefficients:
[tex]\[ 1 (SiCl_4) + 2 (H_2O) + 1 (SiO_2) + 4 (HCl) = 8 \][/tex]
Therefore, the sum of the balanced coefficients is:
[tex]\[ \boxed{8} \][/tex]
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