Consider the following intermediate chemical equations:
[tex]$\begin{array}{l}
2 Na(s)+Cl 2(g) \rightarrow 2 NaCl(s) \
2 Na_2 O(s) \rightarrow 4 Na(s)+O_2(g)
\end{array}$[/tex]
In the final chemical equation, NaCl and [tex]$O _2$[/tex] are the products that are formed through the reaction between [tex]$Na _2 O$[/tex] and [tex]$Cl _2$[/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 (1/2).
D. multiplying the second equation by ([tex]$1 / 4$[/tex]).
Answer (2)
Analyze the given intermediate chemical equations.
Determine the multipliers for each equation to obtain the desired overall reaction.
Eliminate intermediate species by ensuring equal amounts on both sides of the equation.
Simplify the resulting equation to match the target reaction.
The first equation needs to be multiplied by 2 .
Explanation
Understanding the Problem We are given two intermediate chemical equations and asked how to modify them so that when added together, they represent the reaction between N a 2 O and C l 2 to produce N a Cl and O 2 . The given equations are:
2 N a ( s ) + C l 2 ( g ) i g h t ha r p oo n u p 2 N a Cl ( s )
2 N a 2 O ( s ) i g h t ha r p oo n u p 4 N a ( s ) + O 2 ( g )
Setting up the Equations Our goal is to find the correct coefficients to multiply each equation by so that when we add them, we get the overall reaction:
N a 2 O + C l 2 i g h t ha r p oo n u pN a Cl + O 2
Let's denote the multipliers for the first and second equations as x and y , respectively. Then the modified equations are:
2 x N a ( s ) + x C l 2 ( g ) i g h t ha r p oo n u p 2 x N a Cl ( s )
2 y N a 2 O ( s ) i g h t ha r p oo n u p 4 y N a ( s ) + y O 2 ( g )
Eliminating Sodium Adding the modified equations, we get:
2 y N a 2 O ( s ) + x C l 2 ( g ) + 2 x N a ( s ) i g h t ha r p oo n u p 2 x N a Cl ( s ) + 4 y N a ( s ) + y O 2 ( g )
We want to eliminate N a ( s ) from both sides of the equation. This means the amount of N a ( s ) on the reactant side must equal the amount on the product side. Thus, we need 2 x = 4 y , which simplifies to x = 2 y .
Simplifying the Equation Substituting x = 2 y into the combined equation:
2 y N a 2 O ( s ) + 2 y C l 2 ( g ) + 4 y N a ( s ) i g h t ha r p oo n u p 4 y N a Cl ( s ) + 4 y N a ( s ) + y O 2 ( g )
Simplifying, we get:
2 y N a 2 O ( s ) + 2 y C l 2 ( g ) i g h t ha r p oo n u p 4 y N a Cl ( s ) + y O 2 ( g )
Dividing the entire equation by y :
2 N a 2 O ( s ) + 2 C l 2 ( g ) i g h t ha r p oo n u p 4 N a Cl ( s ) + O 2 ( g )
Dividing the equation by 2:
N a 2 O ( s ) + C l 2 ( g ) i g h t ha r p oo n u p 2 N a Cl ( s ) + 2 1 O 2 ( g )
Determining the Multipliers From x = 2 y and the final equation, we need to find x and y . If we multiply the first equation by 2 and the second equation by 1, we have:
4 N a ( s ) + 2 C l 2 ( g ) i g h t ha r p oo n u p 4 N a Cl ( s )
2 N a 2 O ( s ) i g h t ha r p oo n u p 4 N a ( s ) + O 2 ( g )
Adding them gives:
2 N a 2 O ( s ) + 2 C l 2 ( g ) + 4 N a ( s ) i g h t ha r p oo n u p 4 N a Cl ( s ) + O 2 ( g ) + 4 N a ( s )
Canceling 4 N a ( s ) gives:
2 N a 2 O ( s ) + 2 C l 2 ( g ) i g h t ha r p oo n u p 4 N a Cl ( s ) + O 2 ( g )
Dividing by 2 gives:
N a 2 O ( s ) + C l 2 ( g ) i g h t ha r p oo n u p 2 N a Cl ( s ) + 2 1 O 2 ( g )
Therefore, we need to multiply the first equation by 2 and the second equation by 1.
Final Answer The question asks how to alter the intermediate chemical equations. We found that we need to multiply the first equation by 2 and the second equation by 1. Therefore, the correct answer is multiplying the first equation by 2.
Examples
In chemical engineering, balancing equations is crucial for designing industrial processes. For example, if you're designing a process to produce sodium chloride (NaCl) from sodium oxide ( N a 2 O ) and chlorine gas ( C l 2 ), you need to know the exact stoichiometric ratios. This problem demonstrates how to manipulate intermediate reactions to derive the overall balanced equation, ensuring efficient use of reactants and minimizing waste. By correctly balancing the equation, engineers can accurately calculate the required amounts of each reactant to achieve the desired production level of NaCl.
To produce the desired reaction of Na 2 O + Cl 2 → NaCl + O 2 , we need to multiply the first intermediate equation by 2. This adjustment balances the sodium produced while allowing us to effectively combine the reactions. Therefore, the answer is option B: multiplying the first equation by 2.
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