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?

Question

Winston Lowery

Chemistry

3 May, 17:56

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?

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Answers (1)

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Rory Stark · Answer 1

(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