Textbook 7.21

[Megan Singer 3D]

Textbook problem 7.21

7.21 Which of the following plots will be linear? (a) [A] against time for a reaction that is first order in A; (b) [A] against time for a reaction that is zeroth order in A; (c) ln [A] against time for a reaction that is first order in A; (d) 1/[A] against time for a reaction that is second order in A; (e) kr against temperature; (f) initial rate against [A] for a reaction that is first order in A; (g) half-life against [A] for a reaction that is zeroth order in A; (h) half-life against [A] for a reaction that is second order in A.

The linear plots are b, c, d, f, and g.

Can someone explain why e is not linear, why g is linear, and why h is not linear?

[Faaizah Arshad 1H]

e is wrong because k vs temperature is not linear. ln K vs 1/T is linear with a -Ea/R slope.

g is linear because in the half life equation for a zero order reaction, [A] is in the numerator and is directly proportional to half life.

h is not linear because in the half life equation for second order, [A] is in the denominator and is inversely proportional to half life. As concentration decreases, half life increases, so this is not a constant linear graph.