Consider the equations below.
(1) [tex]$Fe _2 O _3(s) \rightarrow 2 Fe ( s )+\frac{3}{2} O _2(g)$[/tex]
(2) [tex]$Fe _2 O _3(s)+3 CO ( g ) \rightarrow 2 Fe ( s )+3 CO _2(g)$[/tex]
Which equation must be added to equation (1) to produce equation (2)?
A. [tex]$CO ( g )+\frac{1}{2} O _2(g) \rightarrow CO _2(g)$[/tex]
B. [tex]$3 CO _2(g) \rightarrow 3 CO ( g )+\frac{3}{2} O _2(g)$[/tex]
C. [tex]$3 CO ( g )+\frac{3}{2} O _2(g) \rightarrow 3 CO _2(g)$[/tex]
Answer (2)
To convert equation (1) into equation (2), we must add option C: 3 CO ( g ) + 2 3 O 2 ( g ) → 3 C O 2 ( g ) . This addition simplifies to exactly match equation (2) upon rearranging and eliminating common terms. Hence, option C is the correct choice.
;
Analyze the given equations (1) and (2).
Test each option by adding it to equation (1).
Check if the resulting equation matches equation (2).
Option 3, 3 CO ( g ) + 2 3 O 2 ( g ) → 3 C O 2 ( g ) , when added to equation (1), produces equation (2). Therefore, the answer is 3 CO ( g ) + 2 3 O 2 ( g ) → 3 C O 2 ( g ) .
Explanation
Understanding the Problem We are given two chemical equations and asked to find which of the provided options, when added to the first equation, results in the second equation. Let's denote the first equation as (1) and the second equation as (2).
Equation 1 Equation (1): F e 2 O 3 ( s ) r i g h t a rro w 2 F e ( s ) + f r a c 3 2 O 2 ( g )
Equation 2 Equation (2): F e 2 O 3 ( s ) + 3 CO ( g ) r i g h t a rro w 2 F e ( s ) + 3 C O 2 ( g )
Finding the Missing Equation We need to find an equation that, when added to equation (1), gives us equation (2). Let's examine the options.
Option 1 Option 1: CO ( g ) + f r a c 1 2 O 2 ( g ) r i g h t a rro wC O 2 ( g )
Option 2 Option 2: 3 C O 2 ( g ) r i g h t a rro w 3 CO ( g ) + f r a c 3 2 O 2 ( g )
Option 3 Option 3: 3 CO ( g ) + f r a c 3 2 O 2 ( g ) r i g h t a rro w 3 C O 2 ( g )
Testing the Options Let's add each option to equation (1) and see which one results in equation (2).
Testing Option 1 Adding Option 1 to equation (1):\ F e 2 O 3 ( s ) + CO ( g ) + f r a c 1 2 O 2 ( g ) r i g h t a rro w 2 F e ( s ) + f r a c 3 2 O 2 ( g ) + C O 2 ( g ) . This does not match equation (2).
Testing Option 2 Adding Option 2 to equation (1):\ F e 2 O 3 ( s ) + 3 C O 2 ( g ) r i g h t a rro w 2 F e ( s ) + f r a c 3 2 O 2 ( g ) + 3 CO ( g ) + f r a c 3 2 O 2 ( g ) . This simplifies to F e 2 O 3 ( s ) + 3 C O 2 ( g ) r i g h t a rro w 2 F e ( s ) + 3 CO ( g ) + 3 O 2 ( g ) . This does not match equation (2).
Testing Option 3 Adding Option 3 to equation (1):\ F e 2 O 3 ( s ) + 3 CO ( g ) + f r a c 3 2 O 2 ( g ) r i g h t a rro w 2 F e ( s ) + f r a c 3 2 O 2 ( g ) + 3 C O 2 ( g ) . We can rearrange this to F e 2 O 3 ( s ) + 3 CO ( g ) + f r a c 3 2 O 2 ( g ) r i g h t a rro w 2 F e ( s ) + 3 C O 2 ( g ) + f r a c 3 2 O 2 ( g ) . Subtracting f r a c 3 2 O 2 ( g ) from both sides gives F e 2 O 3 ( s ) + 3 CO ( g ) r i g h t a rro w 2 F e ( s ) + 3 C O 2 ( g ) , which is equation (2).
Conclusion Therefore, Option 3 is the correct answer.
Examples
In industrial chemistry, understanding how to manipulate chemical equations is crucial for optimizing reaction pathways. For example, in the production of iron from iron oxide, it's important to know which reactants and conditions will lead to the desired product efficiently. This problem demonstrates how combining different reactions can achieve a specific overall transformation, which is a fundamental concept in process design and optimization.
