Concentration-Time Graphs & Rate Constants (College Board AP® Chemistry): Revision Note

A student carried out the following reaction in the laboratory:

A + B → products

After performing the experiment, the student plotted the following graphs: 

Using the graphs above, determine the order of reaction with respect to A

Answer:

• The only graph from these three that is a straight line is Graph II

• A linear ln[A] versus t plot matches the first-order integrated rate law, so the reaction is first order with respect to A

ln [A]_t = -kt + ln [A]₀

• Therefore, it is a first order reaction with respect to A

A student carried out the following reaction in the laboratory:

A + B → products

The reaction is known to be zero order with respect to B. The student plotted the following graph:

Using the graph above, determine the rate constant and write the general rate equation for the reaction

Answer:

• Step 1: Determine the order of reaction with respect to A

  • The plot of 1/[A] versus time is linear, which matches the second-order integrated rate law, so the reaction is second order with respect to A

$\frac{1}{{\left[\mathrm{A}\right]}_{\mathrm{t}}}=\mathrm{kt}+\frac{1}{{\left[\mathrm{A}\right]}_0}$

• Therefore, it is a second order reaction with respect to A

• Step 2: Determine the overall order of reaction

  • Since the statement establishes that it is zero order with respect to B, the overall order is 2

  • Therefore, the general rate equation should look like this:

rate =k [A]²   

• Step 3: Choose two points and write down their coordinates

  • Point 1 (0, 2.0)

  • Point 2 (80, 36.5)

• Step 4: Calculate the slope using the coordinates

  • slope =  $\frac{∆\mathrm{y}}{∆\mathrm{x}}$

  • slope = $\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}$

  • slope = $\frac{36.5-2.0}{80-0}$

  • slope = 0.43 M^-1 s^-1

• Step 5: Calculate the units for the rate constant

  • rate = k [A]²

  • Units of rate = (units of k) × (units of concentration of A)²

  • units of k = $\frac{\mathrm{units}\mathrm{of}\mathrm{rate}}{{\left(\mathrm{units}\mathrm{of}\mathrm{concentration}\mathrm{of}\mathrm{A}\right)}^2}$

  • units of k = $\frac{{\mathrm{Ms}}^{-1}}{{\left(\mathrm{M}\right)}^2}$

  • units of k = $\frac{{\mathrm{Ms}}^{-1}}{\left(\mathrm{M}\right)\left(\mathrm{M}\right)}$

  • units of k = $\frac{s^{-1}}{\mathrm{M}}$
    

  • units of k = M^-1 s^-1

• Step 6: Write down the final rate equation by replacing the calculated value for k

  • rate = k [A]²

  • rate = (0.43 M^-1 s^-1) [A]²