Rate Law and Specific Rate Constant

 

The rate constant, k, is a proportionality constant that shows how the molar concentration of reactants affects the rate of a chemical reaction. By using molar concentrations of the reactants and also the order of the reaction, the rate constant may be determined experimentally. The Arrhenius equation can also be used to compute it. The rate constant’s units are determined by the reaction’s sequence. Because its value is affected by temperature and other circumstances, the rate constant isn’t a genuine constant.

A brief outline

The Arrhenius equation can also be used to express the rate constant:

k = Ae^-Ea/RT

Here, A is the particle collision frequency constant, Ea is the reaction activation energy, R is the gas constant, and T is the temperature. The Arrhenius equation shows that temperature is the most important element in determining the pace of a chemical reaction. The rate constant should, in theory, account for all of the variables that influence reaction rate.

The rate constant, despite its name, is not a constant. Only at a steady temperature does it hold true. Adding or modifying a catalyst, changing the pressure, or even swirling the ingredients might change it. It doesn’t apply if anything other than the concentration of the reactant’s changes in a reaction. Also, because the Arrhenius equation implies reactants are perfect spheres that conduct ideal collisions, it doesn’t work effectively if a reaction comprises big molecules at a high concentration.

Important concepts

Rate Law:

A chemical reaction’s rate law (also known as the rate equation) is an expression that describes the relationship between both the rate of the reaction and the concentrations of the reactants involved.

It’s worth noting that the rate law expression for a specific reaction could only be determined empirically. The balanced chemical equation does not yield the rate law statement.

For a reaction:

aA + bB → cC + dD

Where a, b, c, and d = stoichiometric coefficients of the reactants or products, the rate equation for the reaction is specified by:

Rate ∝ [A]^x[B]^y ⇒ Rate = k[A]^x[B]^y

[A] & [B] = concentrations of the reactants A and B.

x & y = the partial reaction orders for reactants A & B

The proportionality constant ‘k’ = the rate constant of the reaction.

Rate constant for first order

A first-order reaction is one in which the rate of the reaction is linearly proportional to the concentration of only one ingredient. In other terms, a first-order reaction is a chemical reaction whose rate is determined by changes in only one of the reactants’ concentrations. As a result, the order of these reactions is 1.

On a molecular level, a differential rate law can be used to explain a chemical reaction. For a first-order reaction, the differential rate expression is expressed as:

First-Order Reactions Examples

SO₂Cl₂ → Cl₂ + SO₂

2N₂O₅ → O₂ + 4NO₂

2H₂O₂ → 2H₂O + O₂

The reaction of Zero Order

A zero-order chemical reaction takes place in which the rate does not change as the concentration of the reactants changes. As a result, the rate constant of these reactions is always equal to that of the specific reactions.

A zero-order reaction’s differential form is written as:

Rate= −dA/dt = k[A⁰] =k

Where

The rate = reaction’s rate, while k = reaction’s rate constant.

Concentration/time, or M/s, is the unit of the rate constant in a zero-order reaction, where ‘M’ is the molarity and’s is one second.

∴ k = mol L^-1s^-1 is the unit of rate constant.

For elementary reactions, molecular dynamics simulations can be used to derive the rate constant. Calculating the mean residence period of the molecule in the reactant state is one option. Although this strategy is feasible for smaller networks with short residence durations, it is not universally applicable because reactions on the molecular scale are often rare events. The Divided Saddle Theory provides a straightforward solution to this problem. For rate constant computations, various approaches such as the Bennett Chandler technique and Mile stoning have been devised.

FAQs

Question: For a first-order reaction, what is the connection between half-life and the rate constant?

Answer: The half-life of a chemical process is the amount of time it takes for the reactant concentration to reach half of its initial value. The link between the reaction half-life and the reaction rate constant for first-order reactions is provided by the expression:

t1/2 = 0.693/k

Where ‘t1/2’ represents the reaction’s half-life and ‘k’ represents the rate constant.

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What exactly is a rate constant?

The proportionality constant, which explains the link between the molar concentration of the reactants and the pace of a chemical reaction, is known as the rate constant. The rate constant, also defined as the reaction constant or rate of a reaction coefficient, is symbolized by the letter k.

What Impact Does Temperature Have on The Rate Constant?

Temperature has an effect on The rate constant. The rate of the reaction and the rate constant both increase as the temperature rises. When the temperature of a reaction is increased by 10°C, the Rate Constant of the reaction is doubled.

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