Respuesta :
Answer:
The balanced equations are:
[tex]\[ C_2H_6O(l) + 3.5O_2(g) \rightarrow 2CO_2(g) + 3H_2O(g) \][/tex]
[tex]\[ CuS(Aq) + 1.5HNO_3(aq) \rightarrow CuSO_4(aq) + NO_2(g) + H_2O(g) \][/tex]
Explanation:
To balance these chemical equations, we need to ensure that the number of atoms of each element is the same on both sides of the equation.
For the first equation:
[tex]\[ C_2H_6O(l) + O_2(g) \rightarrow CO_2(g) + H_2O(g) \][/tex]
We can start by balancing the carbon atoms. There are 2 carbon atoms on the left side and 1 on the right side, so we need to put a coefficient of 2 in front of [tex]\( CO_2 \)[/tex] to balance the carbon atoms.
[tex]\[ C_2H_6O(l) + O_2(g) \rightarrow 2CO_2(g) + H_2O(g) \][/tex]
Next, let's balance the hydrogen atoms. There are 6 hydrogen atoms on the left side and 2 on the right side, so we need to put a coefficient of 3 in front of [tex]\( H_2O \)[/tex] to balance the hydrogen atoms.
[tex]\[ C_2H_6O(l) + O_2(g) \rightarrow 2CO_2(g) + 3H_2O(g) \][/tex]
Now, let's balance the oxygen atoms. On the left side, we have[tex]\\( O_2 )[/tex], which contributes 2 oxygen atoms per molecule. On the right side, we have [tex]\( CO_2 \)[/tex] (4 oxygen atoms) and[tex]\( H_2O \) (3 oxygen atoms),[/tex] gives us a total of 7 oxygen atoms. To balance this, we need 7/2 molecules of [tex]\( O_2 \)[/tex], which we can write as [tex]\( 7/2 O_2 \) or \( 3.5 O_2 \).[/tex]
[tex]\[ C_2H_6O(l) + 3.5O_2(g) \rightarrow 2CO_2(g) + 3H_2O(g) \][/tex]
Now, the first equation is balanced.
For the second equation:
[tex]\[ CuS(Aq) + HNO_3(aq) \rightarrow CuSO_4(aq) + NO_2(g) + H_2O(g) \][/tex]
We start by balancing the copper atoms. There is 1 copper atom on each side, so no coefficient is needed for [tex]\( CuS \) and \( CuSO_4 \).[/tex]
[tex]\[ CuS(Aq) + HNO_3(aq) \rightarrow CuSO_4(aq) + NO_2(g) + H_2O(g) \][/tex]
Next, let's balance the sulfur atoms. There is 1 sulfur atom on each side, so no coefficient is needed for [tex]\( CuS \) and \( CuSO_4 \).[/tex]
[tex]\[ CuS(Aq) + HNO_3(aq) \rightarrow CuSO_4(aq) + NO_2(g) + H_2O(g) \][/tex]
Now, let's balance the nitrogen atoms. There is 1 nitrogen atom on the left side and 1 on the right side, so no coefficient is needed for [tex]\( HNO_3 \) and \( NO_2 \).[/tex]
[tex]\[ CuS(Aq) + HNO_3(aq) \rightarrow CuSO_4(aq) + NO_2(g) + H_2O(g) \][/tex]
Finally, let's balance the oxygen atoms. On the left side, we have [tex]\( HNO_3 \),[/tex]contributed 3 oxygen atoms per molecule. On the right side, we have [tex]\( NO_2 \)[/tex] (2 oxygen atoms) and [tex]\( H_2O \)[/tex] (1 oxygen atom), giving us a total of 3 oxygen atoms. To balance this, we need 3/2 molecules of [tex]\( HNO_3 \)[/tex], which we can write as [tex]\( 3/2 HNO_3 \) or \( 1.5 HNO_3 \).[/tex]
[tex]\[ CuS(Aq) + 1.5HNO_3(aq) \rightarrow CuSO_4(aq) + NO_2(g) + H_2O(g) \][/tex]
Now, the second equation is balanced.
The balanced equations are:
[tex]\[ C_2H_6O(l) + 3.5O_2(g) \rightarrow 2CO_2(g) + 3H_2O(g) \][/tex]
[tex]\[ CuS(Aq) + 1.5HNO_3(aq) \rightarrow CuSO_4(aq) + NO_2(g) + H_2O(g) \][/tex]
