Integrated Rate Law Video Lessons

Concept:

Problem: Identify what the graphs of [X] versus time and [Y] versus time would look like for various orders.Zero-order [X] vs. tZero-order [Y] vs. tFirst or Second-order [X] vs. tFirst or Second-order [Y] vs. t

FREE Expert Solution

Recall that each straight line plot (A = concentration of reactant) corresponds to:

• [A] vs. time (in s)   Zeroth-order reaction
• ln[A] vs. time (in s)  First-order reaction
• 1/[A] vs. time (in s) Second-order reaction

Integrated rate law:

• Zeroth order reaction:

$\overline{){\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{0}}}}$

• First-order reaction:

$\overline{){\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{0}}}{{\mathbf{e}}}^{\mathbf{-}\mathbf{kt}}}$

• Second-order reaction is as follows:

$\overline{)\frac{\mathbf{1}}{{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{t}}}{\mathbf{=}}{\mathbf{kt}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}}}$

Assuming, X = reactant and Y = product:

Reaction: X → Y

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Problem Details

Identify what the graphs of [X] versus time and [Y] versus time would look like for various orders.

Zero-order [X] vs. t

Zero-order [Y] vs. t

First or Second-order [X] vs. t

First or Second-order [Y] vs. t