Write an equation relating the concentration of a reactant A at t=0 to that at t=t for a first-o

step 1 Good day. The topic is about rate law. Consider a reaction which reactant is a forming product.

Write an equation relating the concentration of a reactant A...

Key Concepts

Rate Constant

The rate constant, denoted as k in the integrated rate laws, quantifies the speed of a reaction. Its units depend on the order of the reaction; for first-order reactions, k has units of s?¹, and for second-order reactions, it has units of M?¹·s?¹. The magnitude of k along with the integrated rate law determines how quickly the concentration of reactants changes over time.

Second-Order Reaction Kinetics

In a second-order reaction where the reaction rate depends on the square of the concentration of a single reactant, the integrated rate law is given by 1/[A]? = 1/[A]? + kt. Here, [A]? is the initial concentration (M), [A]? is the concentration at time t, k is the second-order rate constant (with units of M?¹·s?¹), and t represents the time elapsed (in seconds).

Integrated Rate Law

The integrated rate law is an equation that relates the concentration of a reactant at time t to its initial concentration. It is derived by integrating the differential rate law and is specific to the order of the reaction, providing insight into how reactant concentration decays or accumulates over time.

Reaction Kinetics

Reaction kinetics is the study of the rates of chemical reactions and the factors that affect them. It involves understanding how the concentration of reactants changes with time and how reaction conditions, such as temperature and catalysts, influence these rates.

First-Order Reaction Kinetics

For a first-order reaction, the rate is directly proportional to the concentration of one reactant. The integrated rate law is expressed as ln([A]?/[A]?) = -kt or equivalently [A]? = [A]?·e???, where [A]? is the initial concentration (typically in moles per liter, M), [A]? is the concentration at time t, k is the first-order rate constant (with units of s?¹), and t is the time (in seconds).

Transcript

00:01 Good day.

00:01 The topic is about rate law.

00:03 Consider a reaction which reactant is a forming product.

00:07 The rate of this reaction is expressed in terms of the concentration of the reaction as given by this following rate law.

00:17 R is equal to k, a tiers to the power of m.

00:20 Where your r is rate, k is the rate constant, m is the order of the reaction with respect to the single reactant a and that a is of its own concentration.

00:29 Now we note that.

00:30 That rate can also be expressed in terms of the rate of disappearance of the reactant, or that is d -a -d -t.

00:37 Now, you see that the negative here appears because of the fact that the concentration of a decreases with time, so that d -a -d -t is a negative quantity.

00:47 And so to make r -positive, we need this negative sign here.

00:52 D -a -d -t tells us the differential rate of change of the concentration of the reactant with time.

00:59 And so this can also be termed as the differential rate law.

01:03 Now let us suppose a reaction that is first order, that is am equals 1.

01:10 So that our differential rate law, r, which also is negative d -a -d -t, becomes k times a.

01:21 Or i can rewrite this as d -a -d -t equals negative k -a.

01:29 Now this a here also more appropriately mean can mean d a concentration so that i can have this form...

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