The reaction between sucrose and water to produce fructose and glucose is first order // overall. The data below shows the change in concentration of sucrose over time at 298 K. C12H22011 (aq)sucrose + H2O(l)艹C6H1206(aq)fructose + C6H1206(aq)oucose C12H2201l M Time (minutes) 1.002 0.808 0.630 0.0 60.0 130.0 a. Find the average rate ofdisappearance of C12H22011 from t = 0 min to t-60 min. b. Find the average rate of appearance of fructose from t 0 min to t 60 min. c. Calculate the rate constant, k, for the decomposition of sucrose at 25°C. Include units. d. How long will it take for the concentration of sucrose to drop from 1.002 to 0.212 M? e. What is the half-life for the decomposition of sucrose at 25°C?

First-order reactions are defined as the chemical reactions in which rate of the reaction is linearly dependent on the concentration of only one reactant.

The answers can be explained as:

(a) Rate of appearance of the sucrose from the chemical reaction is:

Rate = =

Rate = 0.00323 m/s

(b) Rate of appearance of Fructose from the given chemical reaction is:

Rate = =

Rate = 0.00323 m/s

(C) Rate constant for the reaction is:

k = 0.00359 minute⁻¹

(d) Time required for the concentration of sucrose to drop from 1.002 to 0.212 M is:

t = 432.6 minutes

(e) The half-life of the decomposition of sucrose at 25°C is:

Half-life =

Half-life = 193 minutes.

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(a)

Rate of appearance of sucrose = - d[C12H22O11] / dt = - ( 0.808 - 1.002 ) / ( 60.0 - 0.0) = 0.00323 M/s

(b)

Rate of appearance of fructose = d[C6H12O6] / dt = (1.002 - 0.808) / (60.0 - 0.0) = 0.00323 M/s

(c)

k = (1 / t ) * ln[A]/[A]t

k = ( 1 / 60.0 ) * ln[1.002 / 0.808]

k = 0.00359 min-1

(d)

0.00359 = ( 1 / t ) * ln[1.002 / 0.212]

t = 432.6 min

(e)

Half life time = 0.693 / k = 0.693 / 0.00359 = 193 min

Explanation:

in the analysis of systems that involve fluid flow, we frequently encounter the combination of properties u and pv.