Apply the concentration jump method to the following Br2 2NO

Apply the concentration jump method to the following:

Br₂+ 2NO=2 BrNO

Assume the mechanism below. 3rd order forwaed and 2nd order reverse

The data in the table below was obtained as total pressure of the gas mixture after adding 39.70 torr to 9.38 torr of bromine in a closed vessel.Note that general chemistry stoichiometric methods may be used to determine partial pressures of all species and ? at each time, and that the equilibrium constant may be determined from the equilibrium partial pressures. Use units of torr and seconds for rate coefficients in this problem.

Time     Ptotal

(sec)      (torr)

0           49.08

5.1       48.00

14.1     46.67

29.2     45.10

47.6     44.00

71.4     43.08

95.3     42.53

170     41.79

?         41.49

Thoroughly evaluate the data, determine the forward and reverse rate coefficients and the equilibrium constant from this data set. You may find it useful to begin with the following statement in your derivation of d?/dt = -kobs·?.

You should be able to show that the reaction rate may be stated as:

-d(PBr2)/dt = -d?/dt = k1·(PBr2)·(PNO)2 - k-1·(PBrNO)2

You should be able to write the partial pressure of each chemical species, Pi, in terms of the equilibrium partial pressure, Pi,e, and ? in deriving your expression for d?/dt = -kobs·?, and ignore second-order and higher terms in ? in your derivation. You should observe that a plot of the experimental data as Ln ? vs. time has some curvature to it, but as ? becomes smaller the approximation obtained by ignoring higher order terms in ? becomes better and the limiting slope of Ln ? vs. time at longer times is a good approximation to -kobs. My recommendation is that you use only the last 2-3 points of the Ln ? vs. time plot for the linear fit.

Finally,

estimate an initial reaction rate for the forward termolecular reaction from the initial pressure change in the data set, and obtain an estimate of the forward rate coefficient from approximation. Compare the result to that obtained from the concentration jump analysis.

Note:

this should help with answer

Solution

Thoroughly evaluate the data, determine the forward and reverse rate coefficients and the equilibrium constant from this data set. You may find it useful to begin with the following statement in your derivation of d/dt = -kobs·.

You should be able to show that the reaction rate may be stated as:

-d(PBr2)/dt = -d/dt = k1·(PBr2)·(PNO)2 - k-1·(PBrNO)2

You should be able to write the partial pressure of each chemical species, Pi, in terms of the equilibrium partial pressure, Pi,e, and in deriving your expression for d/dt = -kobs·, and ignore second-order and higher terms in in your derivation. You should observe that a plot of the experimental data as Ln vs. time has some curvature to it, but as becomes smaller the approximation obtained by ignoring higher order terms in becomes better and the limiting slope of Ln vs. time at longer times is a good approximation to -kobs. My recommendation is that you use only the last 2-3 points of the Ln vs. time plot for the linear fit.

Finally,

estimate an initial reaction rate for the forward termolecular reaction from the initial pressure change in the data set, and obtain an estimate of the forward rate coefficient from approximation. Compare the result to that obtained from the concentration jump analysis.