(a) The reaction C12 H22 O11(a q)+H2 O(l) →C6 H12 O6(a q)+ C6 H12 O6(a q) is first order with in

step 1 In this problem, I have to consider the reaction that I've written here. sucrose plus water equa

(a) The reaction C12 H22 O11(a q)+H2 O(l) →C6 H12 O6(a q)+...

(a) The reaction $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+$ $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)$ is first order with in $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(a q)$ and zero-order in $\mathrm{H}_{2} \mathrm{O}$. At $300 \mathrm{~K}$ the rate constant equals $3.30 \times 10^{-2} \mathrm{~min}^{-1} .$ Calculate the half-life at this temperature. $(\mathbf{b})$ If the activation energy for this reaction is $80.0 \mathrm{~kJ} / \mathrm{mol}$, at what temperature would the reaction rate be doubled?

Key Concepts

Arrhenius Equation

The Arrhenius equation provides a quantitative basis for the temperature dependence of reaction rates by relating the rate constant to the activation energy and temperature. It is expressed as k = A exp(?Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation is essential for predicting how reaction rates change with temperature and for determining the effect of temperature on reaction kinetics.

Activation Energy

Activation energy is the minimum energy that must be overcome for reactants to transform into products during a chemical reaction. It is a critical parameter in kinetics since it influences the temperature sensitivity of a reaction. A higher activation energy typically means that the reaction rate is more sensitive to changes in temperature.

Reaction Order

This concept refers to the exponent to which the concentration of a reactant is raised in the rate law. In a reaction that is first order with respect to one reactant, the rate is directly proportional to its concentration. The reaction order helps in determining how changes in reactant concentration will affect the reaction rate and influences other kinetics parameters, such as half-life.

Half-life of a First Order Reaction

The half-life of a reaction is the time required for the concentration of a reactant to decrease by half. For first order reactions, the half-life is constant and independent of the initial concentration, and it can be calculated using the formula t½ = ln(2)/k, where k is the rate constant. This concept is fundamental in kinetics because it provides a straightforward way to characterize the speed of the reaction.

Rate Constant

The rate constant is a proportionality factor in the rate law that links the rate of a chemical reaction with the concentrations of the reactants. Its value depends on temperature and the nature of the reaction. For first order reactions, the rate constant can be used to determine the half-life, and it is pivotal in comparing reaction speeds under different conditions.

Transcript

Please give Ace some feedback