The information below is for the decomposition of compound B. What is the rate law for this decomposition, and what is the rate constant? [B] (M) 1/[B] (1/M) 0.0111 0.0101 0.0091 0.0081 0.0071 0.0061 0.0051 0.0041 240 220 200 180 8 140 120 100 I 0 0 10 10 20 20 30 30 [B] vs time 40 40 50 time (min) 1/[B] vs time 50 time (min) 60 60 y=-6E-05x+0.0093 R2=0.9494 70 80 y=1.3333x+100 R²=1 70 90 100 80 90 100 In [B] -4.61 -4.7 -4.8 -4.9 -5 -5.1 -5.2 -5.3 -5.4 -5.5 Q 10 20 30 In [B] vs time 40 50 time (min) 60 70 80 y=-0.0087x-4.6522 R²=0.9872 90 100

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Chapter1: Chemical Foundations
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The image contains three graphs analyzing the decomposition of compound B. Each graph plots concentration data over time to determine the reaction order and rate constant.

1. **Graph [B] vs. time:**
   - The y-axis represents the concentration of compound B in molarity (M).
   - The x-axis represents time in minutes.
   - The plotted data points form a downward sloping line.
   - The linear regression equation is \( y = -6E-05x + 0.0093 \) with \( R^2 = 0.9498 \).

2. **Graph ln[B] vs. time:**
   - The y-axis represents the natural logarithm of the concentration of compound B.
   - The x-axis represents time in minutes.
   - The plotted data points form a downward sloping line.
   - The linear regression equation is \( y = -0.0078x - 4.6522 \) with \( R^2 = 0.9872 \).

3. **Graph 1/[B] vs. time:**
   - The y-axis represents the inverse concentration of compound B (1/M).
   - The x-axis represents time in minutes.
   - The plotted data points form an upward sloping line.
   - The linear regression equation is \( y = 1.3333x + 100 \) with \( R^2 = 1 \).

**Analysis:**
- The graph of 1/[B] vs. time shows a perfect linear relationship with an \( R^2 \) value of 1, indicating that the decomposition follows second-order kinetics.
- The rate constant (\( k \)) can be determined from the slope of the line in the 1/[B] vs. time graph: \( k = 1.3333 \) M\(^{-1}\)min\(^{-1}\).
Transcribed Image Text:The image contains three graphs analyzing the decomposition of compound B. Each graph plots concentration data over time to determine the reaction order and rate constant. 1. **Graph [B] vs. time:** - The y-axis represents the concentration of compound B in molarity (M). - The x-axis represents time in minutes. - The plotted data points form a downward sloping line. - The linear regression equation is \( y = -6E-05x + 0.0093 \) with \( R^2 = 0.9498 \). 2. **Graph ln[B] vs. time:** - The y-axis represents the natural logarithm of the concentration of compound B. - The x-axis represents time in minutes. - The plotted data points form a downward sloping line. - The linear regression equation is \( y = -0.0078x - 4.6522 \) with \( R^2 = 0.9872 \). 3. **Graph 1/[B] vs. time:** - The y-axis represents the inverse concentration of compound B (1/M). - The x-axis represents time in minutes. - The plotted data points form an upward sloping line. - The linear regression equation is \( y = 1.3333x + 100 \) with \( R^2 = 1 \). **Analysis:** - The graph of 1/[B] vs. time shows a perfect linear relationship with an \( R^2 \) value of 1, indicating that the decomposition follows second-order kinetics. - The rate constant (\( k \)) can be determined from the slope of the line in the 1/[B] vs. time graph: \( k = 1.3333 \) M\(^{-1}\)min\(^{-1}\).
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