Sucrose is readily hydrolysed to glucose and fructose in acidic solution. The hydrolysis is often monitored by measuring the angle of rotation of plane polarized light passing through the solution. From the angle of rotation the concentration of sucrose can be determined. An experiment on the hydrolysis of sucrose in 0.50 M HCl(aq) produced the following data:

Determine the rate constant of the reaction and the half-life of a sucrose molecule. What is the average lifetime of a sucrose molecule?  

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0 14 39 60 80 110 140 170 210 [sucrose]/(mol dm-³) 0.316 0.300 0.274 0.256 0.238 0.211 0.190 0.170 0.146 t/min