An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Analyze the given chemical equations.
Subtract the first equation from the second to isolate the desired reaction.
Simplify the resulting equation to find the stoichiometric coefficient for O 2 .
The overall equation is P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s ) , so the answer is P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s ) .
Explanation
Problem Analysis We are given two chemical equations:
P 4 ( s ) + 3 O 2 ( g ) → P 4 O 6 ( s )
P 4 ( s ) + 5 O 2 ( g ) → P 4 O 10 ( s )
We want to find the balanced chemical equation for the reaction that produces P 4 O 10 from P 4 O 6 and O 2 . In other words, we want to find the coefficient x in the following equation:
P 4 O 6 ( s ) + x O 2 ( g ) → P 4 O 10 ( s )
Equation Manipulation To find the value of x , we can manipulate the given equations. Subtract the first equation from the second equation:
( P 4 ( s ) + 5 O 2 ( g )) − ( P 4 ( s ) + 3 O 2 ( g )) → P 4 O 10 ( s ) − P 4 O 6 ( s )
This simplifies to:
2 O 2 ( g ) → P 4 O 10 ( s ) − P 4 O 6 ( s )
Finding the Coefficient Rearranging the terms, we get:
P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s )
Thus, the coefficient x for O 2 is 2.
Final Answer The overall equation for the reaction that produces P 4 O 10 from P 4 O 6 and O 2 is:
P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s )
Therefore, the correct answer is:
P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s )
Examples
In chemical manufacturing, understanding how different reactants combine to form specific products is crucial for optimizing processes and ensuring safety. For instance, in the production of phosphorus oxides, knowing the exact amount of oxygen needed to convert P 4 O 6 to P 4 O 10 allows chemists to control the reaction, prevent unwanted byproducts, and maximize the yield of the desired compound. This precise control is essential for large-scale industrial applications where efficiency and purity are paramount. The balanced equation P 4 O 6 ( s ) + 2 O 2 ( g ) → P 4 O 10 ( s ) provides this critical information.
A device delivering a current of 15.0 A for 30 seconds results in a total charge of 450 coulombs. This charge corresponds to approximately 2.81 x 10^21 electrons flowing through the device. The calculation uses the relationship between current, charge, and the charge of an electron.
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