At 35^∘ C, the rate constant for the reaction C12 H22 O11+H2 O ⟶C6 H12 O6+C6 H12 O6is k=6.2 ×10^

step 1 So in this case, we have a specific reaction. In this case, we have to have our temperatures in

At 35^∘ C, the rate constant for the reaction C12 H22 O11+H2...

At $35^{\circ} \mathrm{C}$, the rate constant for the reaction $$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$$is $k=6.2 \times 10^{-5} \mathrm{~s}^{-1}$. The activation energy for the reaction is $108 \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is the rate constant for the reaction at $45^{\circ} \mathrm{C}$ ?

Key Concepts

Temperature Dependence of Reaction Rates

Temperature dependence of reaction rates refers to the phenomenon where the rate at which chemical reactions occur changes with temperature. As temperature increases, a greater proportion of molecules have the necessary energy to overcome the activation barrier, generally leading to an increased reaction rate as predicted by the Arrhenius equation. This concept is central to controlling and optimizing reaction conditions in various chemical processes.

Rate Constant

The rate constant, denoted as k, is a proportionality factor in the rate law of a chemical reaction that quantifies the speed of the reaction. Its value varies with temperature and is influenced by the activation energy and the frequency of molecular collisions. Understanding the rate constant is crucial for predicting how quickly a reaction will proceed under different conditions.

Activation Energy

Activation energy is the specific energy barrier that must be overcome for a reaction to proceed. It represents the minimum energy required to convert reactants into products and is a key parameter in the Arrhenius equation. Higher activation energies generally imply that the reaction rate is more sensitive to changes in temperature.

Arrhenius Equation

The Arrhenius equation is a fundamental formula in chemical kinetics that describes how the rate constant of a reaction depends on temperature. It is expressed as k = A exp(-Ea/RT), where k is the rate constant, 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 helps in understanding and predicting how reaction rates change with temperature variations.

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