Sucrose 1C12H22O112, commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6. At 23 C and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose: Time (min) 3C12H22o11 4 1M2 0 0.316 39 0.274 80 0.238 140 0.190 210 0.146 (a) Is the reaction first order or second order with respect to 3C12H22O114?

Verified step by step guidance

1. <Step 1: Understand the problem.> We need to determine the order of the reaction with respect to sucrose (C_{12}H_{22}O_{11}). The data provided shows the concentration of sucrose at different times. We will use this data to determine if the reaction is first order or second order.
2. <Step 2: Write the rate laws for first and second order reactions.> For a first-order reaction, the rate law is: \( \text{Rate} = k [\text{C}_{12}\text{H}_{22}\text{O}_{11}] \). For a second-order reaction, the rate law is: \( \text{Rate} = k [\text{C}_{12}\text{H}_{22}\text{O}_{11}]^2 \).
3. <Step 3: Use the integrated rate laws.> For a first-order reaction, the integrated rate law is: \( \ln [\text{C}_{12}\text{H}_{22}\text{O}_{11}] = -kt + \ln [\text{C}_{12}\text{H}_{22}\text{O}_{11}]_0 \). For a second-order reaction, the integrated rate law is: \( \frac{1}{[\text{C}_{12}\text{H}_{22}\text{O}_{11}]} = kt + \frac{1}{[\text{C}_{12}\text{H}_{22}\text{O}_{11}]_0} \).
4. <Step 4: Plot the data.> Plot \( \ln [\text{C}_{12}\text{H}_{22}\text{O}_{11}] \) versus time for a first-order reaction and \( \frac{1}{[\text{C}_{12}\text{H}_{22}\text{O}_{11}]} \) versus time for a second-order reaction. The plot that results in a straight line indicates the order of the reaction.
5. <Step 5: Analyze the plots.> Determine which plot is linear. If the plot of \( \ln [\text{C}_{12}\text{H}_{22}\text{O}_{11}] \) versus time is linear, the reaction is first order. If the plot of \( \frac{1}{[\text{C}_{12}\text{H}_{22}\text{O}_{11}]} \) versus time is linear, the reaction is second order.>

Key Concepts

Reaction Order

Reaction order refers to the power to which the concentration of a reactant is raised in the rate law of a chemical reaction. It indicates how the rate of reaction depends on the concentration of reactants. A first-order reaction has a linear relationship between the concentration of one reactant and the rate, while a second-order reaction involves a squared concentration term, indicating a more complex relationship.

Rate Law

The rate law is an equation that relates the rate of a chemical reaction to the concentration of its reactants. It is typically expressed in the form Rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B. Determining the rate law is essential for understanding how changes in concentration affect the speed of the reaction.

Integrated Rate Laws

Integrated rate laws provide a mathematical relationship between the concentration of reactants and time, allowing for the determination of reaction order through experimental data. For first-order reactions, the integrated form is ln[A] = -kt + ln[A]0, while for second-order reactions, it is 1/[A] = kt + 1/[A]0. Analyzing concentration versus time data using these equations helps identify the order of the reaction.