What is the rate of a reaction if the value of [tex]k[/tex] is 0.1, [tex][A][/tex] is 1 M, and [tex][B][/tex] is 2 M? Rate [tex]=K[A]^2[B]^2[/tex]
A. [tex]0.8(mol / L ) / s[/tex]
B. [tex]0.1(mol / L ) / s[/tex]
C. [tex]0.2(mol / L ) / s[/tex]
D. [tex]16(mol / L ) / s[/tex]
Answer (2)
Substitute the given values into the rate equation: Rate = k [ A ] 2 [ B ] 2 = 0.1 \t \t × ( 1 ) 2 × ( 2 ) 2 .
Calculate the rate: Rate = 0.1 × 1 × 4 = 0.4 .
The rate of the reaction is 0.4 ( m o l / L ) / s .
The final answer is 0.4 ( m o l / L ) / s .
Explanation
Problem Setup We are given the rate equation Rate = k [ A ] 2 [ B ] 2 , where k = 0.1 , [ A ] = 1 M , and [ B ] = 2 M . Our goal is to calculate the rate of the reaction by substituting these values into the equation.
Substitution Now, we substitute the given values into the rate equation: R a t e = 0.1 × ( 1 ) 2 × ( 2 ) 2
Calculation Next, we perform the calculation: R a t e = 0.1 × 1 × 4 R a t e = 0.4
Final Answer Therefore, the rate of the reaction is 0.4 ( m o l / L ) / s .
Examples
Understanding reaction rates is crucial in many real-world applications. For instance, in the pharmaceutical industry, knowing the rate at which a drug degrades helps determine its shelf life and proper storage conditions. Similarly, in environmental science, understanding the reaction rates of pollutants helps predict their persistence and impact on ecosystems. In cooking, reaction rates determine how quickly food cooks or spoils. By understanding the factors that influence reaction rates, we can better control and optimize these processes.
The rate of the reaction, calculated using the provided values in the equation Rate = k[A]^2[B]^2, is 0.4 (mol / L) / s. This value does not match any of the provided options, indicating a potential error in the options given. The computation followed proper substitution and calculation steps for reaction rate.
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