Question

Chemists and engineers must be able to predict the changes in chemical concentration in a reaction. A model used for many single-reactant processes is Rate of change of concentration _kCn where C is the chemical concentration and k is the rate constant. The order of the reaction is the value of the exponent n. Solution methods for differential equations (which are discussed in Chapter 9) can show that the solution for a first-order reaction (n = 1) is and the solution for a second-order reaction (n 2) is The following data (from Brown, 1994) describes the gas- phase decomposition of nitrogen dioxide at 300°C. 2NO2 → 2NO + O2 Time t (s) Clmol NO2 L) 0.0100 50 0.0079 100 0.0065 200 0.0048 300 0.0038

Answer 1

The figure shows plots of 1/C and in C versus t Only the plot of 1/C is linear. Therefore the reaction is second-order. To find C(0) and k, we fit a first-order polynomial to the data (1/C, t). The script file is t-p.50, 100,200.3001;C [0.01 ,0 00790006500048,0 00381 y 1/C;coeff-polyfit(t,y,1)C0- The results are C(O) = 1.00396 x 10-2, k = 5.44452 x 10-1. 300 250 은20아 150 100 50 100 150 200 250 300 -4.60 -4.8E 5.2 5.4 -5.6 50 100 150 200