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Akia is balancing the equation [tex]\(Na + H_2O \rightarrow NaOH + H_2\)[/tex]. He tries to find the coefficients that will balance the equation.

How could he find the correct coefficients?

A. By counting each individual atom and making sure the number of each kind of atom is the same in the reactants and the products

B. By counting the total atoms and making sure the number of atoms in the reactants is the same as the number of atoms in the products

C. By counting the total mass of each compound and making sure the reactants have more mass than the products

D. By counting the mass of each atom and making sure the reactants are more massive than the products



Answer :

GinnyAnswer
To balance the chemical equation [tex]\( Na + H_2O \rightarrow NaOH + H_2 \)[/tex], it is essential to follow a systematic approach to ensure the number of atoms of each element is identical on both sides of the equation.

Here's the step-by-step solution to balance the equation:

1. Identify the reactants and the products:
- Reactants: Sodium ([tex]\( Na \)[/tex]) and Water ([tex]\( H_2O \)[/tex]).
- Products: Sodium Hydroxide ([tex]\( NaOH \)[/tex]) and Hydrogen gas ([tex]\( H_2 \)[/tex]).

2. Count the number of atoms for each element in the reactants and the products:
- In the reactants, we have:
- [tex]\( Na \)[/tex]: 1 atom
- [tex]\( H \)[/tex]: 2 atoms (from [tex]\( H_2O \)[/tex])
- [tex]\( O \)[/tex]: 1 atom (from [tex]\( H_2O \)[/tex])
- In the products, we have:
- [tex]\( Na \)[/tex]: 1 atom (from [tex]\( NaOH \)[/tex])
- [tex]\( O \)[/tex]: 1 atom (from [tex]\( NaOH \)[/tex])
- [tex]\( H \)[/tex]: 1 atom (in [tex]\( NaOH \)[/tex]) + 2 atoms (in [tex]\( H_2 \)[/tex]) = 3 atoms

3. Check if the number of atoms for each element matches between reactants and products:
- Sodium ([tex]\( Na \)[/tex]):
- Reactants: 1
- Products: 1
- Oxygen ([tex]\( O \)[/tex]):
- Reactants: 1
- Products: 1
- Hydrogen ([tex]\( H \)[/tex]):
- Reactants: 2
- Products: 3

4. Adjust the coefficients to balance the atoms:
- To balance hydrogen, consider the [tex]\( NaOH \)[/tex] and [tex]\( H_2 \)[/tex] in the products:
- To balance the [tex]\( Na \)[/tex], since [tex]\( Na \)[/tex] is already 1 on both sides, it remains unchanged.
- [tex]\( H \)[/tex] atoms: We need 2 atoms of [tex]\( H \)[/tex] in the reactants to match 3 in the products.
- Since we have 2 hydrogen atoms from water and can form 1 molecule of [tex]\( H_2 \)[/tex]:
[tex]\[ H_2O \rightarrow H_2 + O \][/tex]
- Therefore, adding an additional [tex]\( H_2O \)[/tex] molecule on the reactant side balances out the hydrogen atoms:
[tex]\[ 2Na + 2H_2O \rightarrow 2NaOH + H_2 \][/tex]

5. Verify the equation:
- Reactants: [tex]\( 2Na + 2H_2O \)[/tex]
- Sodium: 2 atoms
- Hydrogen: 4 atoms (2 from each [tex]\( H_2O \)[/tex])
- Oxygen: 2 atoms (1 from each [tex]\( H_2O \)[/tex])
- Products: [tex]\( 2NaOH + H_2 \)[/tex]
- Sodium: 2 atoms
- Hydrogen: 4 atoms (2 from [tex]\( NaOH \)[/tex] and 2 from [tex]\( H_2 \)[/tex])
- Oxygen: 2 atoms (1 from each [tex]\( NaOH \)[/tex])

Now the equation is balanced:
[tex]\[ 2Na + 2H_2O \rightarrow 2NaOH + H_2 \][/tex]

The coefficients that balance the equation are:
- [tex]\( Na \)[/tex]: 1 (however, when exactly balanced, you find 2 [tex]\( Na \)[/tex])
- [tex]\( H_2O \)[/tex]: 2
- [tex]\( NaOH \)[/tex]: 2
- [tex]\( H_2 \)[/tex]: 1

Therefore, the correct answer to find the coefficients that balance the equation is:
- By counting each individual atom and making sure the number of each kind of atom is the same in the reactants and the products.

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