32 Questions
What is the rate equation for a first-order reaction?
d[A]/dt = -k[A]
What is the integrated form of the rate equation for a first-order reaction?
ln[A] = -αkt + ln[A]0
What is the unit of the rate constant for a first-order reaction?
reciprocal time, s-1
What is the plot of ln[A] versus t for a first-order reaction?
a straight line
What is the slope of the plot of ln[A] versus t for a first-order reaction?
-αk
What is the initial concentration of the reactant in the rate equation for a first-order reaction?
[A]0
What is the expression for the rate of a first-order reaction?
VR = -k[A]
What is the relationship between the rate constant and the concentration of the reactant in a first-order reaction?
k is independent of [A]
What is the expression for the integral rate equation of a first-order reaction in terms of the extent of the reaction?
ln(a / (a - x)) = αkt
What is the integrated rate equation for a second-order reaction?
αkt = 1/[A] - 1/[A]0
What is the unit of the rate constant (k) in a first-order reaction?
s^-1
What is the plot that is linear for a second-order reaction?
1/[A] versus t
What is the characteristic of a pseudo-first-order reaction?
The reaction involves two reactants with different concentrations.
What is the rate equation for a reaction with two reactants, A and B, where the reaction is first order with respect to both A and B?
rate = k[A][B]
What is the half-life equation for a second-order reaction?
t1/2 = 1/(αk[A]0)
What is the definition of a second-order reaction?
A reaction whose rate is proportional to the square of the concentration of A.
What is the condition for the rate equation to be equivalent to the integrated rate equation for a second-order reaction?
[A]0 = [B]0
What is the expression for the rate law of a second-order reaction involving one reactant?
d[A] / dt = -k[A]^2
What is the unit of the rate constant (k) in a second-order reaction?
M^-1s^-1
What does the slope of the plot of 1/[A] versus t represent?
The second-order rate constant
What is the dependence of the half-life of a second-order reaction on the initial concentration of the reactant?
The half-life is inversely proportional to the initial concentration
What is the expression for the concentration of A at time t in a second-order reaction?
[A]t = [A]0 / (1 + kt[A]0)
What is the relationship between the half-life (t1/2) and the rate constant (k) in a first-order reaction?
t1/2 = 0.693 / k
What is the unit of the second-order rate constant?
M-2s-1
What is the units of the rate constant for a second-order reaction?
concentration^-1 time^-1
What is the form of the integrated rate equation for a second-order reaction in which the initial reactants are not in stoichiometric proportions?
kt = ln([A][B]o) / ([A]o - [B]o)
What is the plot of versus t for a second-order reaction in which the initial reactants are not in stoichiometric proportions?
a linear plot of ln([A]/[B]) versus t
What is the substitution in the integrated equation for the reaction A → Products?
a instead of [A]o and (a-x) instead of [A]
What is the integral rate equation for the reaction A → Products in terms of the extent of reaction x?
kt = 1/(a-x) - 1/a
What is the substitution in the integrated equation for the reaction A + B → Products?
a and b instead of [A]o and [B]o, and (a-x) and (b-x) instead of [A] and [B]
What is the integral rate equation for the reaction A + B → Products in terms of the extent of reaction x?
kt = ln(a(b-x)/b(a-x))
What is the expression for the rate of reaction VR when the initial reactants are not in stoichiometric proportions?
VR = -k[A][B]
Study Notes
First Order Reactions
- The rate law for a first-order reaction is:
d[A]/dt = -k[A] - The integrated rate equation is:
ln[A] = -αkt + ln[A]0 - The rate constant (k) has units of reciprocal time (time)-1, s-1
- A plot of ln[A] versus t is a straight line with a slope of -αk
Derivation of Integral Rate Equation for First Order Reactions
- The reaction is: A → products
- At time = 0, [A] = [A]0
- At time = t, [A] = [A]t
- Substituting [A]0 and [A]t into the integrated equation, we get:
ln(a) = αkt
Pseudo First Order Reactions
- The reaction is: A → products
- The rate law is:
d[A]/dt = -k[A] - Pseudo first-order reactions occur when the concentration of one reactant is much higher than the other
Second Order Reactions
- The rate law for a second-order reaction is:
d[A]/dt = -k[A]^2 - The integrated rate equation is:
1/[A] = αkt + 1/[A]0 - The rate constant (k) has units of concentration-1 time-1
- A plot of 1/[A] versus t is a straight line with a slope of αk
Second Order Reactions with One Reactant
- The reaction is: A → products
- The rate law is:
d[A]/dt = -k[A]^2 - The integrated rate equation is:
1/[A] = αkt + 1/[A]0 - The half-life (t1/2) is:
t1/2 = 1/(αk[A]0)
Second Order Reactions with Two Reactants
- The reaction is: A + B → products
- The rate law is:
d[A]/dt = -k[A][B] - If [A]0 = [B]0, then the rate equation is:
d[A]/dt = -k[A]^2 - If [A]0 ≠ [B]0, then the integrated rate equation is:
kt = ln([A]/[B])
Exercise 1.2
- Derive the integral rate equation for the second-order reaction in terms of the extent of reaction x
- For the reaction A → products, the integral rate equation is:
kt = 1/(a-x) - 1/a - For the reaction A + B → products, the integral rate equation is:
kt = ln(b(a-x)/a(b-x))
Half-Life
- The half-life (t1/2) is the time taken for the concentration of the reactant to decrease to half its initial value
- For a first-order reaction, the half-life is:
t1/2 = 0.693/k - For a second-order reaction, the half-life depends on the initial concentration of the reactant
This quiz covers the basics of integrated rate laws, including first-order reactions and rate equations. Topics include the definition of first-order reactions, rate equations, and integration.
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