Question

e unknown-order irreversible reaction takes place in a batch reactor. The initial concentrations A (CAD) is 10 mol dm-3, and the reaction constant, k1, is 0.5 (its unit is unknown). After multiple experiments, the concentraion change of A over the reaction is measured as below. Please, determine the order of reaction and explain your reasoning. AAR t = np.array([1, 2, 3, 4,5, 6, 7, 8, 9, 101) CA = np.array([0.499, 0.353, 0.289, 0.250.0.224.0.204.0.189, 0.177.0.167,0.158)

Answer 1

solution con unknowon orden crearsible Reaction with the reaction s were les w e Nora G A "OR... Taking Mole Valance over the reactor, wie Moles In = Moles out + Accumulation + Disappearance by chemical For Batch Reactor Moles In=0 Reaction. th Reactor acopo Moles out -03608D 0 - 0 + DNA + (-ha)V. V- Volime of of A the is time it to both sides. La - UNA = (-RAV - MA = Rate of destruction Let us asume an wth order kinetics to – r= k CAM (CA is the concentration of M A in the fluid at -da - KCAM NA/V CA at ting Taking loge on both ln 1-dA) = lnk + n ln A. y = c +m2 1 + Straight loss Thus if we plot a graph of ln (da) on yanis and en A on nanis. Ini ate +mXe Straighplot.

CA kyn 0.930252 2.5929 600 vo AWNA dCf/dt In(-dCA/dt) INCA 0.499 -0.146 -1.92415 -0.69515 0.353 -0.064 -2.74887 -1.04129 0.289 -0.039 -3.24419 -1.24133 0.25 -0.026 -3.64966 -1.38629 0.224 -0.02 -3.91202 -1.49611 0.204 -0.015 -4.19971 -1.58964 0.189 -0.012 -4.42285 -1.66601 0.177 -0.01 -4.60517 -1.73161 0.167 -0.009 -4.71053 -1.78976 0.158 0.0158 #NUM! -1.84516 10 In(-dCa/dt) vs Inca -1.5 -0.5 -0.5 0 y = 2.5929x - 0.0723 R2 = 0.9986 In(-dCa/dt) -4 i u InCA

weaker We will get y intercept as enke and slope as n. From graph slope is 2.5929. .: Expoimentally order of reaction n=2.5929 and rate constant enke = -0.0723 L k n = exp(-0.0723) - 0.930252 k = 0.930252 (mol 1-2.5929 time- time-l. lor =0.930252 (mol -0.5929 We can easily fit the experimental data to the straight line mode to easily get the rate constant and order of reaction. That is the easiest way possible. In a batch Reactor Input = 0, output= 0 because we charge a beed in the batch reactor let it reacte for some amount of time and take out the product after certain time. This is nota continuous process. Accumulation dNA - Number of moles that is getting converted in unit time
the rate constant is 0.930252 (mol/L)^-0.5929* time^-1

And the order of reaction is 2.5929