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Sagot :
To determine which chemical equation is properly balanced, we need to verify that the number of each type of atom on the left side (reactants) matches the number of each type of atom on the right side (products). Let's consider each equation given:
1. Equation 1:
\(2 \text{Al} + 3 \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{Cu}\)
- Left Side:
- Al: 2 atoms
- Cu: 3 atoms (from 3 CuSO_4)
- SO_4: 3 groups (from 3 CuSO_4)
- Right Side:
- Al: 2 atoms (from Al_2(SO_4)_3)
- Cu: 3 atoms
- SO_4: 3 groups (from Al_2(SO_4)_3)
Both sides have equal numbers of Al, Cu, and SO_4. This equation is balanced.
2. Equation 2:
\( \text{Al} + 3 \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{Cu}\)
- Left Side:
- Al: 1 atom
- Cu: 3 atoms (from 3 CuSO_4)
- SO_4: 3 groups (from 3 CuSO_4)
- Right Side:
- Al: 2 atoms (from Al_2(SO_4)_3)
- Cu: 3 atoms
- SO_4: 3 groups (from Al_2(SO_4)_3)
The numbers of Al atoms are not equal on both sides: 1 Al (left) and 2 Al (right). This equation is not balanced.
3. Equation 3:
\( 2 \text{Al} + \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{Cu}\)
- Left Side:
- Al: 2 atoms
- Cu: 1 atom (from 1 CuSO_4)
- SO_4: 1 group (from 1 CuSO_4)
- Right Side:
- Al: 2 atoms (from Al_2(SO_4)_3)
- Cu: 3 atoms
- SO_4: 3 groups (from Al_2(SO_4)_3)
The numbers of Cu and SO_4 groups are not equal on both sides: 1 Cu and 1 SO_4 (left) versus 3 Cu and 3 SO_4 (right). This equation is not balanced.
4. Equation 4:
\( 2 \text{Al} + 3 \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \text{Cu}\)
- Left Side:
- Al: 2 atoms
- Cu: 3 atoms (from 3 CuSO_4)
- SO_4: 3 groups (from 3 CuSO_4)
- Right Side:
- Al: 2 atoms (from Al_2(SO_4)_3)
- Cu: 1 atom
- SO_4: 3 groups (from Al_2(SO_4)_3)
The numbers of Cu atoms are not equal on both sides: 3 Cu (left) versus 1 Cu (right). This equation is not balanced.
From this review, we can conclude that only the first equation is properly balanced:
[tex]\[2 \text{Al} + 3 \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{Cu}\][/tex]
1. Equation 1:
\(2 \text{Al} + 3 \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{Cu}\)
- Left Side:
- Al: 2 atoms
- Cu: 3 atoms (from 3 CuSO_4)
- SO_4: 3 groups (from 3 CuSO_4)
- Right Side:
- Al: 2 atoms (from Al_2(SO_4)_3)
- Cu: 3 atoms
- SO_4: 3 groups (from Al_2(SO_4)_3)
Both sides have equal numbers of Al, Cu, and SO_4. This equation is balanced.
2. Equation 2:
\( \text{Al} + 3 \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{Cu}\)
- Left Side:
- Al: 1 atom
- Cu: 3 atoms (from 3 CuSO_4)
- SO_4: 3 groups (from 3 CuSO_4)
- Right Side:
- Al: 2 atoms (from Al_2(SO_4)_3)
- Cu: 3 atoms
- SO_4: 3 groups (from Al_2(SO_4)_3)
The numbers of Al atoms are not equal on both sides: 1 Al (left) and 2 Al (right). This equation is not balanced.
3. Equation 3:
\( 2 \text{Al} + \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{Cu}\)
- Left Side:
- Al: 2 atoms
- Cu: 1 atom (from 1 CuSO_4)
- SO_4: 1 group (from 1 CuSO_4)
- Right Side:
- Al: 2 atoms (from Al_2(SO_4)_3)
- Cu: 3 atoms
- SO_4: 3 groups (from Al_2(SO_4)_3)
The numbers of Cu and SO_4 groups are not equal on both sides: 1 Cu and 1 SO_4 (left) versus 3 Cu and 3 SO_4 (right). This equation is not balanced.
4. Equation 4:
\( 2 \text{Al} + 3 \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \text{Cu}\)
- Left Side:
- Al: 2 atoms
- Cu: 3 atoms (from 3 CuSO_4)
- SO_4: 3 groups (from 3 CuSO_4)
- Right Side:
- Al: 2 atoms (from Al_2(SO_4)_3)
- Cu: 1 atom
- SO_4: 3 groups (from Al_2(SO_4)_3)
The numbers of Cu atoms are not equal on both sides: 3 Cu (left) versus 1 Cu (right). This equation is not balanced.
From this review, we can conclude that only the first equation is properly balanced:
[tex]\[2 \text{Al} + 3 \text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{Cu}\][/tex]
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