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Consider the following intermediate chemical equations:

[tex]\[
\begin{array}{l}
2 \, Na(s) + Cl_2(g) \rightarrow 2 \, NaCl(s) \\
2 \, Na_2O(s) \rightarrow 4 \, Na(s) + O_2(g)
\end{array}
\][/tex]

In the final chemical equation, [tex]\(\text{NaCl}\)[/tex] and [tex]\(\text{O}_2\)[/tex] are the products that are formed through the reaction between [tex]\(\text{Na}_2\text{O}\)[/tex] and [tex]\(\text{Cl}_2\)[/tex]. Before you can add these intermediate chemical equations, you need to alter them by:

A. multiplying the second equation by 2.
B. multiplying the first equation by 2.
C. multiplying the first equation by [tex]\(\frac{1}{2}\)[/tex].
D. multiplying the second equation by [tex]\(\frac{1}{4}\)[/tex].



Answer :

GinnyAnswer
To solve this problem, let's analyze the intermediate chemical equations and determine the necessary alterations to obtain the final balanced equation.

The given intermediate chemical equations are:

1. [tex]\( 2 Na (s) + Cl_2 (g) \rightarrow 2 NaCl (s) \)[/tex]
2. [tex]\( 2 Na_2 O (s) \rightarrow 4 Na (s) + O_2 (g) \)[/tex]

We are looking for the products [tex]\( NaCl \)[/tex] and [tex]\( O_2 \)[/tex] formed from the reaction between [tex]\( Na_2 O \)[/tex] and [tex]\( Cl_2 \)[/tex].

First, let’s balance the equations individually and combine them.

1. The reaction [tex]\( 2 Na (s) + Cl_2 (g) \rightarrow 2 NaCl (s) \)[/tex] shows that 2 sodium atoms react with 1 molecule of chlorine to produce 2 molecules of sodium chloride.

2. The reaction [tex]\( 2 Na_2 O (s) \rightarrow 4 Na (s) + O_2 (g) \)[/tex] indicates that 2 formula units of sodium oxide decompose into 4 sodium atoms and 1 molecule of oxygen gas.

To combine these equations properly, we need to ensure that the number of sodium atoms is balanced.

Since we need 8 Na atoms (from 4 [tex]\( Na_2 O \)[/tex]) to react with chlorine:

- Multiply the first equation by 2 to balance the Na atoms with the second equation:
[tex]\[ 2 \times [ 2 Na (s) + Cl_2 (g) \rightarrow 2 NaCl (s) ] \][/tex]
This becomes:
[tex]\[ 4 Na (s) + 2 Cl_2 (g) \rightarrow 4 NaCl (s) \][/tex]

- Multiply the second equation by 2 to maintain consistency in the number of sodium atoms:
[tex]\[ 2 \times [ 2 Na_2 O (s) \rightarrow 4 Na (s) + O_2 (g) ] \][/tex]
This becomes:
[tex]\[ 4 Na_2 O (s) \rightarrow 8 Na (s) + 2 O_2 (g) \][/tex]

Now, we can combine these balanced equations:

1. [tex]\( 4 Na_2 O (s) \rightarrow 8 Na (s) + 2 O_2 (g) \)[/tex]
2. [tex]\( 4 Na (s) + 2 Cl_2 (g) \rightarrow 4 NaCl (s) \)[/tex]

Combining these adjusted equations gives us:
[tex]\[ 4 Na_2 O (s) + 2 Cl_2 (g) \rightarrow 4 NaCl (s) + 2 O_2 (g) \][/tex]

Therefore, the correct alterations needed to combine these equations effectively are:

- Multiply the second equation by 2.
- Multiply the first equation by 2.

The correct answer is:
1. Multiply the second equation by 2.
2. Multiply the first equation by 2.

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