What is the final chemical equation from the following intermediate chemical equations?
[tex]
\begin{array}{l}
P_4 O_6(s) \rightarrow P_4(s)+3 O_2(g) \
P_4(s)+5 O_2(g) \rightarrow P_4 O_{10}(s)
\end{array}
[/tex]
Answer (2)
The final chemical equation derived from the given intermediate equations is P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s ) . This equation shows how phosphorus trioxide reacts with oxygen to produce phosphorus pentoxide. It simplifies the two provided reactions into a single overall reaction.
;
Analyze the given chemical equations.
Identify the equations that directly convert reactants to products.
Compare the equations and choose the simplest one.
The final chemical equation is: P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s ) .
Explanation
Problem Analysis We are given a set of chemical equations and need to determine the final chemical equation. We should analyze the given equations to see if any of them directly represent the final chemical equation or if we need to combine them.
Examining the Equations Let's examine the provided equations:
P 4 O 6 ( s ) r i g h t a rro w P 4 ( s ) + 3 O 2 ( g )
P 4 ( s ) + 5 O 2 ( g ) r i g h t a rro w P 4 O 10 ( s )
P 4 O 6 ( s ) + 2 O 2 ( g ) r i g h t a rro w P 4 O 10 ( s )
P 4 O 6 ( s ) + 8 O 2 ( a ) r i g h t a rro w 2 P 4 ( s ) + P 4 O ( s )
P 4 O 6 ( s ) + 15 O 2 ( g ) r i g h t a rro w P 4 ( s ) + P 4 O 10 ( s )
P 4 O 6 ( s ) + ( 5/3 ) O 2 ( g ) r i g h t a rro w P 4 O 10 ( s )
Identifying Potential Final Equations Equation 3: P 4 O 6 ( s ) + 2 O 2 ( g ) r i g h t a rro w P 4 O 10 ( s ) and Equation 6: P 4 O 6 ( s ) + ( 5/3 ) O 2 ( g ) r i g h t a rro w P 4 O 10 ( s ) both show the direct conversion of P 4 O 6 and O 2 to P 4 O 10 . These are likely candidates for the final equation. However, they have different coefficients for O 2 . We should check if they are equivalent by multiplying equation 6 by 3.
Checking for Equivalence Multiplying equation 6 by 3, we get: 3 \[P _4 O _6(s)+(5 / 3) O _2(g) rightarrow P _4 O _{10}(s)\] 3 P 4 O 6 ( s ) + 5 O 2 ( g ) r i g h t a rro w 3 P 4 O 10 ( s ) .
This is not the same as equation 3. However, equation 3 is the simplest equation that directly converts P 4 O 6 and O 2 to P 4 O 10 .
Considering Simplicity Equation 6, P 4 O 6 ( s ) + ( 5/3 ) O 2 ( g ) r i g h t a rro w P 4 O 10 ( s ) , is also a valid equation, but it involves a fractional coefficient. To avoid fractional coefficients, we can multiply the entire equation by 3, resulting in 3 P 4 O 6 ( s ) + 5 O 2 ( g ) r i g h t a rro w 3 P 4 O 10 ( s ) . However, we are looking for the simplest equation.
Final Chemical Equation Therefore, the simplest and most likely final chemical equation is: P 4 O 6 ( s ) + 2 O 2 ( g ) r i g h t a rro w P 4 O 10 ( s )
Examples
In chemical manufacturing, understanding the final chemical equation is crucial for optimizing reaction conditions and predicting product yields. For instance, if P 4 O 6 is a starting material and P 4 O 10 is the desired product, knowing the balanced equation P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s ) allows chemists to calculate the exact amount of oxygen needed to convert a given amount of P 4 O 6 completely into P 4 O 10 , minimizing waste and maximizing efficiency. This principle applies broadly in industrial chemistry, where precise control over reactions is essential for economic and environmental reasons.
