Question

1. the following data was collected for the decomposition of chlorine monoxide into chlorine and oxygen at 25 degree Celsius:(show your works)

time (s) 0 10 20 30 40 100 200

ClO (M) 15.0 7.01 4.76 3.52 2.71 1.20 0.65

a. create and attach three seperate plots using this data and the integrated form of the rate law for a 0th, 1st, and 2nd order reaction?

b. what is the order of this decomposition reaction?

c. determine the rate law and the rate constant

2. the gas phase decomposition of 2.50M ammonia into nitrogen and hydrogen is studied at 856 degree celsius yielding data: ( show your works)

time (s) 200 300 600 750 800 900 1000

NH3 (M) 1.85 1.65 1.05 0.74 0.65 0.40 0.26

a. create and attach three seperate plots using this data and the integrated form of the rate law for a 0th, 1st, and 2nd order reaction?

b. what is the reaction order of this decomposition reaction?

c. determine the rate law and the rate constant

d.  determine the half-life for this reaction

3. list the Arrhenius equation and define each term (show your works)

Answer 1

Let the rate (-r)= -dCA/dt= KCAⁿ

Where n is order of the reaction and A is ClO2.

For zero order reaction , the integrated expression becomes ( CAO is initial concentration and CA is concentration at any time t).

CA= CAO- Kt   (1) ( So a plot of CA Vs t gives a straight line passing through origin)

For a 1^st order reaction

-ln(1-XA)= Kt (2) where XA= 1-CA/CAO

Or ln CA = lnCAO- Kt ( So a plot of –ln(1-XA) vs t gives straight line whose slope is K)

For a second order reaction

1/CA= 1/CAO+ Kt (3) ( the plot of 1/CA Vs t gives a straight line whose slope is K).

All the three equatins are plotted and shown below

Zero order reaction plot

1st order reaction plot

2nd order reaction plot

This suggets the decomposition of Cl2O is second order   The slope gives the rate constant whose value is 0.007/M2.sec The rate law is -r = 0.007 [ClO2]²

2.

Let the rate (-r)= -dCA/dt= KCAⁿ

Where n is order of the reaction and A is NH3.

For zero order reaction , the integrated expression becomes ( CAO is initial concentration and CA is concentration at any time t).

CA= CAO- Kt   (1) ( So a plot of CA Vs t gives a straight line passing through origin)

For a 1^st order reaction

-ln(1-XA)= Kt (2) where XA= 1-CA/CAO

Or ln CA = lnCAO- Kt ( So a plot of –ln(1-XA) vs t gives straight line whose slope is K)

For a second order reaction

1/CA= 1/CAO+ Kt (3) ( the plot of 1/CA Vs t gives a straight line whose slope is K).

The plots for the data on decomposition of NH3 for all the three orders are shown below

1st order

The reaction is zero order with rate constant 0.002 M/sec. The rate law -r =0.002

1st order reaction plot

2nd order reaction plot

So the reaction w.r.t ClO2 is 2nd order while the reaction w.r.t. NH3 is Zero order.

Arhenius Equation is K= Ko*e^-Ea/RT

K= Rate constant, Ko= Frequency work and Ea = activation energy and R= gas constant, T= Temperature in K