Consider the equations below.
(1) $Ca ( s )+ CO _2(g)+\frac{1}{2} O _2(g) \rightarrow CaCO _3(s)$
(2) $2 Ca ( s )+ O _2(g) \rightarrow 2 CaO ( s )$
How should you manipulate these equations so that they produce the equation below when added? Check all that apply.
$CaO(s)+CO_2(g) \rightarrow CaCO_3(s)$
A. Reverse the direction of equation (2)
B. Multiply equation (1) by 3
C. Multiply equation (2) by $1 / 2$
Answer (2)
To produce the target equation C a O ( s ) + C O 2 ( g ) → C a C O 3 ( s ) , we need to reverse equation (2) and multiply it by 2 1 . Therefore, the correct options are A and C.
;
Reverse equation (2): 2 C a ( s ) + O 2 ( g ) → 2 C a O ( s ) becomes 2 C a O ( s ) → 2 C a ( s ) + O 2 ( g ) .
Multiply the reversed equation (2) by 2 1 : C a O ( s ) → C a ( s ) + 2 1 O 2 ( g ) .
Add the modified equation (2) to equation (1) and simplify by cancelling out C a ( s ) and 2 1 O 2 ( g ) from both sides.
The resulting equation is C a O ( s ) + C O 2 ( g ) → C a C O 3 ( s ) .
The correct manipulations are reversing equation (2) and multiplying it by 2 1 .
Explanation
Understanding the Problem We are given two chemical equations: (1) C a ( s ) + C O 2 ( g ) + 2 1 O 2 ( g ) → C a C O 3 ( s ) (2) 2 C a ( s ) + O 2 ( g ) → 2 C a O ( s ) We want to manipulate these equations to obtain: C a O ( s ) + C O 2 ( g ) → C a C O 3 ( s ) We need to determine which operations (reversing, multiplying) on equations (1) and (2) will result in the target equation when the manipulated equations are added together.
Reversing Equation (2) Let's start by reversing equation (2): 2 C a O ( s ) → 2 C a ( s ) + O 2 ( g )
Multiplying by 1/2 Next, multiply the reversed equation (2) by 2 1 :
2 1 × [ 2 C a O ( s ) → 2 C a ( s ) + O 2 ( g )] ⇒ C a O ( s ) → C a ( s ) + 2 1 O 2 ( g )
Adding the Equations Now, add the modified equation (2) to equation (1): [ C a ( s ) + C O 2 ( g ) + 2 1 O 2 ( g ) → C a C O 3 ( s )] + [ C a O ( s ) → C a ( s ) + 2 1 O 2 ( g )] This results in: C a ( s ) + C O 2 ( g ) + 2 1 O 2 ( g ) + C a O ( s ) → C a C O 3 ( s ) + C a ( s ) + 2 1 O 2 ( g )
Simplifying the Equation Simplify the resulting equation by cancelling out common terms on both sides of the reaction. We can cancel C a ( s ) and 2 1 O 2 ( g ) from both sides: C a ( s ) + C O 2 ( g ) + 2 1 O 2 ( g ) + C a O ( s ) → C a C O 3 ( s ) + C a ( s ) + 2 1 O 2 ( g ) C a O ( s ) + C O 2 ( g ) → C a C O 3 ( s ) This is the target equation.
Checking Multiplication by 3 Now let's check if multiplying equation (1) by 3 is a valid operation. Multiplying equation (1) by 3 gives: 3 × [ C a ( s ) + C O 2 ( g ) + 2 1 O 2 ( g ) → C a C O 3 ( s )] ⇒ 3 C a ( s ) + 3 C O 2 ( g ) + 2 3 O 2 ( g ) → 3 C a C O 3 ( s ) This equation, when combined with any manipulation of equation (2), will not result in the target equation.
Conclusion Therefore, the correct manipulations are reversing equation (2) and multiplying it by 2 1 .
Examples
Understanding how to manipulate chemical equations is crucial in various fields, such as environmental science and materials engineering. For instance, in designing carbon capture technologies, chemists need to combine different reactions to convert carbon dioxide into stable compounds. By manipulating and combining equations, they can optimize the process to maximize efficiency and minimize waste. This involves adjusting reaction conditions and using catalysts to favor the desired products, ultimately contributing to reducing greenhouse gas emissions and mitigating climate change.
