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Which additional product balances the reaction [tex]$H_2SO_4 + 2NaOH \rightarrow Na_2SO_4 + \qquad$[/tex]?

A. [tex]2H_2O[/tex]
B. [tex]2OH[/tex]
C. [tex]H_2O_2[/tex]
D. [tex]H_3O[/tex]

Answer :

- Count the number of atoms of each element on the left side of the reaction.
- Count the number of atoms of each element on the right side of the reaction, including $Na_2SO_4$.
- Compare the number of atoms of each element on both sides of the reaction.
- Identify the missing atoms on the right side of the reaction and determine that the missing product is $\boxed{2 H _2 O}$.

### Explanation
1. Understanding the Problem
We are given the chemical reaction: $H_2SO_4 + 2NaOH \rightarrow Na_2SO_4 + ?$ and we need to find the missing product that balances the reaction.

2. Counting Atoms on the Left Side
Let's count the number of atoms of each element on the left side of the equation:
- Hydrogen (H): 2 (from $H_2SO_4$) + 2 (from $2NaOH$) = 4
- Sulfur (S): 1 (from $H_2SO_4$)
- Oxygen (O): 4 (from $H_2SO_4$) + 2 (from $2NaOH$) = 6
- Sodium (Na): 2 (from $2NaOH$)

3. Counting Atoms on the Right Side (Initial)
Now let's count the number of atoms of each element on the right side of the equation, considering only $Na_2SO_4$:
- Sodium (Na): 2
- Sulfur (S): 1
- Oxygen (O): 4

4. Identifying Missing Atoms
Comparing both sides, we see that:
- Sodium (Na): 2 = 2 (balanced)
- Sulfur (S): 1 = 1 (balanced)
- Hydrogen (H): 4 on the left, 0 on the right (unbalanced)
- Oxygen (O): 6 on the left, 4 on the right (unbalanced)
We need to find a product that contains 4 H atoms and 2 O atoms.

5. Evaluating the Options
Let's examine the given options:
- $2H_2O$: Contains 4 H atoms and 2 O atoms. This balances the equation.
- $2OH$: Contains 2 O atoms and 2 H atoms. This does not balance the equation.
- $H_2O_2$: Contains 2 H atoms and 2 O atoms. This does not balance the equation.
- $H_3O$: Contains 3 H atoms and 1 O atom. This does not balance the equation.

6. Final Answer
Therefore, the missing product is $2H_2O$. The balanced chemical equation is: $H_2SO_4 + 2NaOH \rightarrow Na_2SO_4 + 2H_2O$

7. Conclusion
The additional product that balances the reaction is $\boxed{2 H _2 O}$

### Examples
Balancing chemical equations is crucial in many real-world applications, such as in the pharmaceutical industry when synthesizing new drugs, in environmental science when studying pollution, and in manufacturing when optimizing chemical processes. Ensuring that the number of atoms is conserved on both sides of a chemical reaction allows scientists and engineers to accurately predict the amount of reactants needed and products formed, leading to efficient and safe chemical processes.

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Rewritten by : Jeany