--%>
Assignment Help - homework help

Describe First Order Rate Equation

The integrated forms of the first order rate equations are conveniently used to compare concentration time results with this rate equation.

Rate equations show the dependence of the rate of the reaction on concentration can be integrated to give expressions for the dependence of the concentrations on time. We generally use the integrated rate equation that is obtained to deduce the order of a reaction.

A first order reaction is one for which, at a given temperature, the rate of the reaction depends only on the first power of the concentration of a single reacting species. If the concentrations of this species is represented by c (for solutions, the units of moles per litre are ordinarily used), and if the volume of the system remains essentially constant during the course of the reaction, the first order rate equation can be written

-dc/dt = kc

The rate of constant k is then a positive quantity and has the units of the reciprocal of time.

Integrated rate equation: the experimental results obtained in a study of the rate of a reaction are usually values of c or some related to c at various times. Such data can best be compared with the integrated form of the first order rate equation. If the concentration at time t = 0 is c0, and if at some later time t the concentration has fallen to c, the integration gives

481_First order reactions.png 

With -In (c/c0) = In (c0/c), the integration can be written as

In c0/c = kt

Sometimes a more convenient form is

In c = -kt + In c0

A reaction can therefore be said to be first order if a plot of In (c0/c) or In c versus t gives a straight line. If a straight line is obtained, the slope of the line can be used to give the value of the rate constant k. an alternative to this graphical procedure is the calculation of a value of kfrom the individual measurements of c at the various times t, for example. The reaction is classified as first order if all the data lead to essentially the same values for k, that is, if it is satisfies with k as a constant.

Example: the rate of conversion of tert-butyl bromide to tert-butyl alcohol, (CH3)3CBr + H2O 1598_First order reactions1.png (CH3)3COH + HBr, has been studied and some concentration-time results are found in table given below. Verify that the reaction is first order, and deduce the values of the rate constant at the two temperatures.

Solution: from the data at each temperature we calculate In (c0/c) values. Then the graphical display shows a plot of In (c0/c) versus t is constructed. The straight lines, each going through the origin show that at both temperatures the data conform to the integrated first order relation. The slopes give the values of the rate constants 

K = 0.00082 min-1 = 0.137 × 10-4 s-1 [25°C]    

K = 0.0142 min-1 = 2.37 × 10-4 s-1 [50°C]    

Concentration of tert butyl bromide as a function of time for the reaction (CH3)3CBr + H2O 1598_First order reactions1.png (CH3)3COH + HBr in a 10% water, 90% acetone solvent

At 25°C  At 50°C
Time, h (CH3)3CBr, Mol L-1 Time, min (CH3)3CBr, Mol L-1
0 0.1039 0 0.1056
3.15 0.0896 9 0.0961
6.20 0.0776 18 0.0856
10.0 0.0639 27 0.0767
13.5 0.0529 40 0.0645
18.3 0.0353 54 0.0536
26.0 0.0270 72 0.0432
30.8 0.0207 105 0.0270
37.3 0.0142 135 0.0174
43.8 0.0101 180 0.0089

   Related Questions in Chemistry

  • Q : Modes of concentration Which of the

    Which of the given modes of expressing concentration is fully independent of temperature: (1) Molarity (2) Molality (3) Formality (4) Normality Choose the right answer from above.

    		•
  • Q : Number of moles of potassium chloride

    Choose the right answer from following. The number of moles of KCL in 1000ml of 3 molar solution is: (a)1 (b)2 (c)3 (d)1.5

    		•
  • Q : How can enzymes act as catalyst?

    Enzymes are complex proteinous substances, produced by living bodies, such as act as catalysis in the physiological reactions. The enzymes are, also called biochemical catalysts and the phenomenon is known as bio-chemical catalysis because numerous reactions that occur the bodies of animals and p

    		•
  • Q : Laws of Chemical Combination Laws of

    Laws of Chemical Combination- In order to understand the composition of the compounds, it is necessary to have a theory which accounts for both qualitative and quantitative observations during chem

    		•
  • Q : Moles of HCl present in .70 L of a .33

    Detail the moles of HCl which are present in .70 L of a .33 M HCl solution?

    		•
  • Q : Mole fraction of hydrogen Give me

    Give me answer of this question. In a mixture of 1 gm H2 and 8 gm O2 , the mole fraction of hydrogen is: (a) 0.667 (b) 0.5 (c) 0.33 (d) None of these

    		•
  • Q : Problem on convection coefficient An

    An experiment to determine the convection coefficient associated with airflow over the surface of a thick stainless steel casting involves insertion of thermocouples in the casting at distances of 10 mm and 20 mm from the surface.  When the experiment was perform

    		•
  • Q : What is synthetic rubber and how it

    To meet human needs, scientists have started preparing synthetic rubbers. Besides having similar properties as natural rubbers they are tougher, more flexible and more durable than natural rubber. They are capable of getting stretched to twice its length. Though, it reverts to its original shape

    		•
  • Q : Explain equilibrium and molecular

    The equilibrium constant can be treated as a particular type of molecular distribution. Consider the simplest gas-phase reaction, one in which molecules of A are converted to molecules of B. the reaction, described by the equation

    Q : Explain the polymers and its types.

    Polymers are the chief products of modern chemical industry which form the backbone of present society. Daily life without the discovery and varied applications of polymers would not have been easier and colourful. The materials made of polymers find multifarious uses and applications in all walk

    		•