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From the following data for the decomposition of N_(2)O_(5) in carbon tetrachloride solution at 321 K, show that the reaction is of the first order and calculate the rate constant. {:("Time (in minutes)",,,,:,,,10,,,15,,,20,,,25,,,oo),("Vol. of "O_(2)" evolved "("in "cm^(3)),,,,:,,,6.30,,,8.95,,,11.40,,,13.50,,,34.75):} |
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Answer» Solution :If the reaction is of the first order, it MUST obey theequation : `k=(2.303)/(t)log""(a)/(a-x)=(2.303)/(t)log""(V_(oo))/(V_(oo)-V_(t))` In the present case, we are given that `V_(oo)=34.75" cm"^(3)` The value of k at each INSTANT can be calculated as follows : `{:("t(min)",,,V_(t),,,V_(oo)-V_(t),,,k=(2.303)/(t)log""(V_(oo))/(V_(oo)-V_(t))),(10,,,6.30,,,34.75-6.30=28.45,,,k=(2.303)/(10min)log""(34.75)/(28.45)=0.01997min^(-1)),(15,,,8.95,,,34.75-8.95=25.80,,,k=(2.303)/(15min)log""(34.75)/(25.80)=0.01985min^(-1)),(20,,,11.40,,,34.75-11.40=23.35,,,k=(2.303)/(20min)log""(34.75)/(23.35)=0.01987min^(-1)),(25,,,13.50,,,34.75-13.50=21.25,,,k=(2.303)/(25min)log""(34.75)/(21.25)=0.01967min^(-1)):}` Since the value of k comes to be nearly CONSTANT, hence given reaction is of the first order. The AVERAGE value of the constant `=0.01984" minute"^(-1)` |
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