Consider the following first order reaction taking place at 308 K in 0.5 N HCl Sucrose to Glucose + Fructose At t = 0, the initial total rotation of the mixture is 32.4^(@). After 10 minutes, the total rotation of sucrose is 28.8^(@). If the rotation of sucrose per mole is 85^(@), that of glucose is 74^(@) and fructose is -86.04^(@), what will be the half-life of the reaction ?

Consider the following first order reaction taking place at 308 K in 0

1.	Consider the following first order reaction taking place at 308 K in 0.5 N HCl Sucrose to Glucose + Fructose At t = 0, the initial total rotation of the mixture is 32.4^(@). After 10 minutes, the total rotation of sucrose is 28.8^(@). If the rotation of sucrose per mole is 85^(@), that of glucose is 74^(@) and fructose is -86.04^(@), what will be the half-life of the reaction ?
Answer» Solution :Suppose rotation per mole of sucrose, GLUCOSE and FRUCTOSE are `r_(1),r_(2)` and `r_(3)` respectively Sucrose `to` Glucose + Fructose `{:("At "t=0,,,a,,,0,,,0),("At time "t,,,a-x,,,x,,,x):}` `ar_(1)=32.4" or "a=(32.4)/(r_(1))=(32.4)/(85)=0.38` `(a-x)r_(1)+xr_(2)-xr_(3)=28.8` `ar_(1)+x(r_(2)+r_(3)-r_(1))=28.8` or `x(r_(2)+r_(3)-r_(1))=28.8-32.4=-3.6` `x(74-86.04-85)=-3.6" or "x=0.037` For a first order reaction `k=(2.303)/(t)log""(a)/(a-x)=(2.303)/(10)log""(0.38)/(0.38-0.037)=9.21xx10^(-3)min^(-1)` `t_(1//2)=(0.693)/(k)=(0.693)/(9.21xx10^(-3))=75.2" min"`