Chemical Kinetics

What is the primary subject of study in chemical kinetics?

Chemical kinetics deals with the study of reaction rates and their mechanisms.

What question about a chemical reaction does thermodynamics answer?

Thermodynamics predicts the feasibility of a reaction, i.e., whether it will occur or not (related to $\Delta G < 0$).

What aspect of a chemical reaction is determined by chemical equilibrium?

Chemical equilibrium determines the extent to which a reaction will proceed before reaching a state of balance.

The Greek word 'kinesis', from which 'kinetics' is derived, means _.

movement

How can the rate of a chemical reaction be defined in terms of concentration?

It is the change in concentration of a reactant or product per unit time.

What is the difference between an average rate and an instantaneous rate of reaction?

The average rate is calculated over a significant time interval ($\Delta C / \Delta t$), while the instantaneous rate is the rate at a specific moment in time ($dC/dt$).

How is the instantaneous rate of a reaction determined from a concentration vs. time graph?

It is determined by calculating the slope of the tangent to the curve at that specific point in time.

For a reaction $R \rightarrow P$, the rate of disappearance of R is expressed as _.

Rate = $-\frac{\Delta[R]}{\Delta t}$

Why is a negative sign used when expressing the rate of reaction with respect to a reactant?

Since the concentration of a reactant decreases over time, its change ($\Delta$[Reactant]) is negative; the negative sign makes the overall rate a positive quantity.

For the general reaction $aA + bB \rightarrow cC + dD$, what is the expression for the rate of reaction in terms of reactant A?

Rate = $-\frac{1}{a} \frac{d[A]}{dt}$

For the general reaction $aA + bB \rightarrow cC + dD$, what is the expression for the rate of reaction in terms of product C?

Rate = $+\frac{1}{c} \frac{d[C]}{dt}$

What are the typical units for the rate of a reaction when concentration is in mol $L^{-1}$ and time is in seconds?

The units are mol $L^{-1} s^{-1}$.

List five factors that can affect the rate of a chemical reaction.

Concentration of reactants, temperature, presence of a catalyst, nature of reactants, and surface area.

What is a rate law or rate expression?

It is an equation that represents the rate of reaction in terms of the molar concentration of reactants, with each term raised to a power.

In the general rate law, Rate = $k[A]^x[B]^y$, what does the constant 'k' represent?

'k' is the rate constant, or specific rate constant, a proportionality constant specific to the reaction at a given temperature.

The sum of the powers of the concentration terms in the rate law expression (e.g., x + y) is called the _ of the reaction.

overall order

How must the order of a reaction be determined?

The order of a reaction must be determined experimentally; it cannot be predicted from the stoichiometry of the balanced equation.

A reaction in which the stoichiometric coefficients in the balanced equation are equal to the experimentally determined orders of the reactants is known as a(n) _ reaction.

elementary

If the experimentally determined orders of reactants are not equal to their stoichiometric coefficients, the reaction is known as a(n) _ reaction.

complex

What does it mean if a reaction is zero order with respect to a reactant?

It means the rate of the reaction is independent of the concentration of that reactant.

What are the possible values for the order of a reaction?

The order of a reaction can be positive, negative, zero, or a fraction.

What are the units of the rate constant (k) for a zero-order reaction?

mol $L^{-1} s^{-1}$ (or concentration time$^{-1}$).

What are the units of the rate constant (k) for a first-order reaction?

$s^{-1}$ (or time$^{-1}$).

What are the units of the rate constant (k) for a second-order reaction?

$L mol^{-1} s^{-1}$ (or concentration$^{-1}$ time$^{-1}$).

Term: Molecularity

Definition: The number of reacting species (atoms, ions, or molecules) that collide simultaneously to bring about a chemical reaction in an elementary step.

How does molecularity differ from the order of a reaction?

Molecularity is a theoretical concept applied to elementary steps and must be a positive integer (1, 2, or 3), while order is an experimental quantity for the overall reaction and can be zero, fractional, or negative.

Reactions with a molecularity greater than three are very rare. Why?

The probability of a simultaneous and effective collision between more than three particles is extremely small.

What is the rate-determining step (RDS) in a complex reaction?

The rate-determining step is the slowest elementary step in the reaction mechanism, which controls the overall rate of the reaction.

What is the primary purpose of using an integrated rate law?

It provides a relationship between the concentration of reactants and time, avoiding the need to determine the instantaneous rate graphically.

What is the integrated rate law for a zero-order reaction?

$[R] = -kt + [R]0$, where $[R]$ is concentration at time t, and $[R]0$ is the initial concentration.

A plot of $[R]$ versus time for a zero-order reaction yields a straight line. What is the slope of this line?

The slope is equal to $-k$ (the negative of the rate constant).

What is the integrated rate law for a first-order reaction, expressed using natural logarithm (ln)?

$ln[R] = -kt + ln[R]_0$

What is the integrated rate law for a first-order reaction, expressed using common logarithm (log)?

$log[R] = -\frac{kt}{2.303} + log[R]_0$

For a first-order reaction, a plot of $ln[R]$ versus time produces a straight line. What does the slope of this line represent?

The slope is equal to $-k$ (the negative of the rate constant).

The exponential form of the first-order integrated rate law is _.

$[R] = [R]_0 e^{-kt}$

What is the half-life ($t_{1/2}$) of a reaction?

It is the time required for the concentration of a reactant to decrease to one-half of its initial value.

What is the formula for the half-life of a zero-order reaction?

$t{1/2} = \frac{[R]0}{2k}$

How does the half-life of a zero-order reaction depend on the initial concentration?

The half-life is directly proportional to the initial concentration of the reactant.

What is the formula for the half-life of a first-order reaction?

$t_{1/2} = \frac{0.693}{k}$

How does the half-life of a first-order reaction depend on the initial concentration?

The half-life of a first-order reaction is independent of the initial concentration.

Reactions like the hydrolysis of an ester in a large excess of water, which are bimolecular but behave as first-order, are called _ reactions.

pseudo-first-order

What is the general rule of thumb for the effect of a 10 K increase in temperature on a reaction's rate constant?

For many chemical reactions, the rate constant nearly doubles with a 10 K (or 10°C) rise in temperature.

What is the Arrhenius equation, which relates the rate constant (k) to temperature (T)?

$k = A e^{-Ea/RT}$, where A is the Arrhenius factor, $Ea$ is the activation energy, R is the gas constant, and T is the absolute temperature.

Term: Activation Energy ($E_a$)

Definition: The minimum amount of energy required for reactants to transform into the activated complex and proceed to form products.

In the Arrhenius equation, what does the pre-exponential factor 'A' represent?

'A' is the Arrhenius factor or frequency factor, which is related to the frequency of collisions between reactant molecules.

What is an activated complex?

It is an unstable, high-energy intermediate state that is formed during the conversion of reactants to products.

How does an increase in temperature affect the Maxwell-Boltzmann distribution of molecular energies?

The curve broadens and shifts to the right, increasing the fraction of molecules that possess energy equal to or greater than the activation energy.

The logarithmic form of the Arrhenius equation is $ln(k) = -\frac{E_a}{R}(\frac{1}{T}) + ln(A)$. A plot of $ln(k)$ vs. $1/T$ yields a straight line. What is its slope?

The slope of the line is equal to $-E_a/R$.

How does a catalyst increase the rate of a chemical reaction?

A catalyst provides an alternative reaction pathway or mechanism with a lower activation energy ($E_a$).

Does a catalyst affect the overall Gibbs free energy change ($\Delta G$) or the equilibrium constant of a reaction?

No, a catalyst does not alter the thermodynamics ($\Delta G$) or the final equilibrium position; it only increases the rate at which equilibrium is reached.

According to collision theory, what two conditions must be met for a collision between reactant molecules to be effective?

The colliding molecules must possess sufficient kinetic energy (threshold energy) and have the proper orientation.

In collision theory, the number of collisions per second per unit volume of the reaction mixture is known as _.

collision frequency (Z)

Collision theory introduces a factor 'P' to account for the orientation requirement of collisions. What is this factor called?

It is called the probability factor or steric factor.

The equation $Rate = P Z{AB} e^{-Ea/RT}$ is the mathematical representation of which theory?

Collision Theory.

The initial concentration of reactant A is 0.55 mol $L^{-1}$. After 30 seconds, its concentration is 0.31 mol $L^{-1}$. What is the average rate of reaction over this interval?

The average rate is $-(0.31 - 0.55) / 30 = 0.008$ mol $L^{-1} s^{-1}$.

For a reaction with the rate law Rate = $k[A]^{1/2}[B]^2$, what is the overall order of the reaction?

The overall order is $1/2 + 2 = 2.5$.

For the decomposition of N2O5, which follows first-order kinetics, what would be the shape of a plot of $[N2O5]$ versus time?

The plot would be an exponential decay curve. An exponential decay curve shows a quantity rapidly decreasing at first, then slowing down over time, approaching a limit (like zero) but never quite reaching it

If the thermal decomposition of $N2O5$ ($2N2O5(g) \rightarrow 4NO2(g) + O2(g)$) is studied in a constant volume container, how is the total pressure related to the progress of the reaction?

The total pressure increases over time because 2 moles of gaseous reactant produce 5 moles of gaseous products.

For the reaction $2HI(g) \rightarrow H2(g) + I2(g)$, how is the rate of disappearance of HI related to the rate of appearance of $H_2$?

The rate of disappearance of HI is twice the rate of appearance of $H2$ ($-\frac{1}{2} \frac{d[HI]}{dt} = +\frac{d[H2]}{dt}$).

What is the relationship between threshold energy, activation energy, and the energy of reacting species?

Threshold energy = Activation Energy + energy already possessed by the reacting species.