Identify '$p$', '$q$' and '$r$' in the following balanced reaction:
[tex]\stackrel{\text { Heat }}{p Pb(NO_3)_{2(s)}-\cdots--\ \textgreater \ q PbO_{(s)}+rNO_{2(g)}+O_{2(g)}}[/tex]
A. $2,2,4$
B. $2,4,2$
C. $2,4,4$
D. $4,2,2$
Answer (2)
Balance the number of Pb atoms: p = q .
Balance the number of N atoms: 2 p = r .
Balance the number of O atoms: 6 p = q + 2 r + 2 .
Solve the system of equations to find p = 2 , q = 2 , and r = 4 . The answer is 2 , 2 , 4 .
Explanation
Analyzing the Reaction Let's analyze the given chemical reaction and balance it to find the correct coefficients.
Unbalanced Reaction The unbalanced reaction is: pP b ( N O 3 ) 2 ( s ) → qP b O ( s ) + r N O 2 ( g ) + O 2 ( g )
Balancing Strategy We need to find the values of p , q , and r that balance the equation. We will balance the number of atoms for each element (Pb, N, and O).
Balancing Equations
Balance Pb atoms: p = q
Balance N atoms: 2 p = r
Balance O atoms: 6 p = q + 2 r + 2
Substitution Substitute p for q and 2 p for r in the oxygen balance equation: 6 p = p + 2 ( 2 p ) + 2
Simplification Simplify the equation: 6 p = p + 4 p + 2
Solving for p Solve for p :
6 p = 5 p + 2 p = 2
Finding q and r Since p = 2 , then q = 2 and r = 2 p = 4 .
Balanced Reaction Therefore, the balanced reaction is: 2 P b ( N O 3 ) 2 ( s ) → 2 P b O ( s ) + 4 N O 2 ( g ) + O 2 ( g )
Final Answer The coefficients are p = 2 , q = 2 , and r = 4 . Therefore, the correct answer is A.
Examples
Balancing chemical equations is crucial in various real-world applications, such as environmental science, where it helps in understanding and controlling pollution. For instance, in designing catalytic converters for cars, engineers use balanced equations to optimize the conversion of harmful gases like nitrogen oxides ( N O x ) into less harmful substances like nitrogen and oxygen. This ensures that the converter operates efficiently, reducing air pollution and improving air quality. Similarly, in industrial chemistry, balancing equations is essential for calculating the precise amounts of reactants needed to produce a desired amount of product, maximizing yield and minimizing waste.
In the balanced reaction of lead(II) nitrate decomposing, the coefficients are found to be p = 2 , q = 2 , and r = 4 . Therefore, the correct choice is A: 2 , 2 , 4 .
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