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Sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),$ commonly called table sugar, undergoes hydrolysis (reaction with water) to produce fructose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ and glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$$$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$$fructose glucoseThis reaction is of considerable importance in the candy industry. First, fructose is sweeter than sucrose. Second, a mixture of fructose and glucose, called invert sugar, does not crystallize, so the candy containing this sugar would be chewy rather than brittle as candy containing sucrose crystals would be. (a) From the following data determine the order of the reaction. (b) How long does it take to hydrolyze 95 percent of sucrose? (c) Explain why the rate law does not include $\left[\mathrm{H}_{2} \mathrm{O}\right]$ even though water is a reactant. $$\begin{array}{cc}\hline \text { Time (min) } & {\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right]} \\\hline 0 & 0.500 \\60.0 & 0.400 \\96.4 & 0.350 \\157.5 & 0.280 \\\hline\end{array}$$

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(a) first-order(b) $814 \mathrm{min}$(c) Water is the solvent in this reaction so it is present in large excess compared to the reactants. Thus, the concentration of water almost remains constant so the reaction rate becomes independent of its concentration.

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

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Lectures

22:42

In probability theory, the conditional probability of an event A given that another event B has occurred is defined as the probability of A given B, written as P(A|B). It is a function of the probability of B, the probability of A given B, and the probability of B.

04:55

In chemistry, kinetics is the study of the rates of chemical reactions. The rate of a reaction is the change in concentration of a reactant over time. The rate of reaction is dependent on the concentration of the reactants, temperature, and the activation energy of the reaction.

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Sucrose $\left(\mathrm{C}_…

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The hydrolysis of the suga…

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Common sugar, sucrose, bre…

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The metabolism of table su…

to determine the order of this reaction. The easiest thing to do is to plot the concentration as a function of time. In the natural log of the concentration is a function of time and went over. The concentration is a function of time. That's what I did here. I took the time and I took the concentration and I plotted them. And I get this line right here. I did the same thing with the natural log of the concentration as a function of time to get this one and then one over the concentration as a function of time to get this one in order to determine the order of the reaction, we want the best straight line. The best straight line is determined by the R squared value. The R squared value closest toe one is going to be the best straight line because the R squared value for the plotting of the natural log of concentration of the function of time is the one closest to one. Then we can determine the order by recognizing that when the natural log of the concentration plotted as a function of time gives us a straight line, its first order. If however it were, the concentration is a function of time that gives us the best straight line with the R squared value closest toe one. It would be zero order if it were one over. The concentration is a function of time that gave it the best straight line with R squared value closest toe one. It would be second order because we know it's first order than the equation of the line actually gives us information associated with the rate constant. The negative of this slope is the rate constant. This this will be needed for part B, where in part B, we have to calculate the concentration after 95% has been converted. If 95% has been converted, then 5% is left over 5% out of one is five. So if we start with a 11 as our concentration initially, then at Time t the concentration would be five of that when 95% has reacted. So this then is theme beginning of the first order. Integrated rate law with a natural log of the concentration at Time T divided by the initial concentration, is equal to negative K and K is going to be the negative of this negative slope. So the positive 0.37 to a few more significant figures, which you're not seeing on this graph we get 0.0 3681 So natural log of concentration at time T divided by concentration of time zero equals negative K t. And all we have to do then is rearrange the equation and solve for T. And when we do that, we get 814 minutes. Part C then asks why water? It's not part of the rate constant. Well, water, although it's a reactant, is it's such a high concentration that as the reaction proceeds, its concentration does not change significantly. If it's concentration does not change significantly, then it itself the water itself does not affect the rate of the reaction.

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