Reaction Rate and Kinetics: Definitions, Laws, and Calculations

What is reaction rate?

The change in concentration of a reactant or product per unit time.

Why are reactant rates written with a negative sign?

Reactant concentrations decrease over time. The negative sign makes the overall reaction rate positive.

Why are product rates written with a positive sign?

Product concentrations increase as the reaction proceeds.

How do you write a reaction rate expression using coefficients?

Divide each substance's concentration change over time by its stoichiometric coefficient. Use negative signs for reactants and positive signs for products.

For Cl2 + 3F2 → 2ClF3, what is the full rate expression?

Rate = -Δ[Cl2]/Δt = -(1/3)Δ[F2]/Δt = (1/2)Δ[ClF3]/Δt.

What is the difference between rate of disappearance and concentration change for a reactant?

Rate of disappearance is reported as positive, but the concentration change Δ[reactant]/Δt is negative.

How do you convert a known disappearance rate into an appearance rate?

Multiply the given positive rate by the coefficient of the new substance divided by the coefficient of the given substance.

If 5 Br− produce 3 Br2 and Br− disappears at 3.5 × 10^-4 M/s, what is the appearance rate of Br2?

(3/5)(3.5 × 10^-4) = 2.1 × 10^-4 M/s.

What is the general differential rate law?

Rate = k[A]^m[B]^n, where k is the rate constant and m and n are experimentally determined reaction orders.

What does first order in a reactant mean?

Its concentration has an exponent of 1 in the rate law. Doubling only that reactant doubles the rate.

What does second order in a reactant mean?

Its concentration has an exponent of 2. Doubling only that reactant quadruples the rate.

What does zero order in a reactant mean?

Its concentration has an exponent of 0. Changing that reactant's concentration does not change the rate.

How do you calculate overall reaction order?

Add the exponents in the rate law. For rate = k[A]^2[B], the overall order is 3.

If a reaction is first order in NO and first order in O3, what is its rate law?

Rate = k[NO][O3]. Each concentration is raised to the first power.

How do you calculate rate when the rate law and concentrations are given?

Substitute the rate constant and concentrations into the rate law, including all exponents, then multiply and report the correct units.

What is the rate for k = 2.20 × 10^7 M^-1 s^-1, [NO] = 3.3 × 10^-6 M and [O3] = 5.9 × 10^-7 M?

Rate = k[NO][O3] = 4.3 × 10^-5 M/s.

How do you identify zero order from an experimental table?

The concentration changes between experiments, but the rate stays constant.

For a reaction that is zero order in its only reactant, how do you find k?

Rate = k[A]^0 = k, so k equals the measured reaction rate.

If a zero-order rate is 0.005 M/s, what is k?

k = 0.005 M/s.

How do you determine the order in one reactant from a table?

Compare two experiments where only that reactant changes and the others remain constant. Compare how much the rate changes.

If doubling a reactant doubles the rate, what is its order?

First order, because 2^1 = 2.

If doubling a reactant quadruples the rate, what is its order?

Second order, because 2^2 = 4.

If doubling a reactant leaves the rate unchanged, what is its order?

Zero order, because 2^0 = 1.

For rate = k[NO]^2[Cl2], how do you solve for k?

Rearrange: k = Rate / ([NO]^2[Cl2]). Substitute the values from one experiment.

How do you determine the units of k?

Rearrange the rate law to solve for k, then divide the rate units by the concentration or pressure units raised to their exponents.

What are the units of k for zero-, first-, second- and third-order reactions using M and seconds?

Zero: M/s; first: s^-1; second: M^-1 s^-1; third: M^-2 s^-1.

What are the units of k for a third-order reaction using pressure in atm?

atm^-2 s^-1, because (atm/s) / atm^3 = atm^-2 s^-1.

What is half-life?

The time required for half of the initial amount of a reactant or radioactive isotope to remain.

What are the half-life equations for zero-, first- and second-order reactions?

Zero: t1/2 = [A]0/(2k); first: t1/2 = 0.693/k; second: t1/2 = 1/(k[A]0).

For second-order decay, k = 2.42 M^-1 s^-1 and [A]0 = 0.500 M. What is the half-life?

t1/2 = 1/(2.42 × 0.500) = 0.826 seconds.

For radioactive first-order decay, how do you find k from the half-life?

k = 0.693/t1/2. For fluorine-18 with t1/2 = 109.7 min, k = 0.00632 min^-1.

What is the first-order integrated rate law for fraction remaining?

ln([A]t/[A]0) = -kt. The ratio is the fraction remaining; multiply by 100 for percent remaining.

When should you use the first-order integrated rate law instead of the half-life equation?

Use it when a problem asks for the fraction or percentage remaining after a given time, or the time required to reach a specified fraction remaining.

What is the difference between percent decayed and percent remaining?

Percent remaining = 100% − percent decayed. For example, 99.99% decayed means 0.01% remains, or a fraction of 0.0001.

Why must time units match the units of k?

The product kt must be unitless. If k is in min^-1, time must be in minutes; if k is in s^-1, time must be in seconds.

How do you convert 5.59 hours into minutes for a kinetics problem?

5.59 × 60 = 335.4 minutes.

Can you use coefficients in a balanced overall equation to determine experimental reaction orders?

Not generally. Reaction orders must come from experimental rate data unless the reaction is specified as an elementary step.

What is reaction rate?

The change in concentration of a reactant or product per unit time.

What is average reaction rate?

The average reaction rate over a given period of time during the reaction. It is calculated using change in concentration divided by change in time.

What is instantaneous reaction rate?

The reaction rate at one specific moment during the reaction. On a concentration vs. time graph, it is determined from the slope of the tangent line at that moment.

What is initial reaction rate?

The instantaneous rate at the very beginning of a reaction, when products first begin to form (t = 0).

How can you distinguish average, instantaneous, and initial reaction rates on an exam?

Average = over a time interval; instantaneous = at one specific moment; initial = at the very start of the reaction. Initial rate is a special type of instantaneous rate.