A gas mixture containing CH3 fragments, C2H6 molecules, and an inert gas (He) was prepared at 600 K with a total pressure of 5.42 atm. The elementary reaction
has a second-order rate constant of 3.0 × 104/M · s. Given that the mole fractions of CH3 and C2H6 are 0.00093 and 0.00077, respectively, calculate the initial
Interpretation:
The initial rate of the given reaction at the given temperature has to be calculated.
Concept introduction:
Rate of the reaction is the change in the concentration of reactant or a product with time. It can be varied in accordance with temperature, pressure, concentration, presence of catalyst, surface area
Rate equation for the general reaction
Rate constants are independent of concentration but depend on other factors, most notably temperature.
The reaction with the faster rate will have the larger rate constant.
Order of a reaction: The sum of exponents of the concentrations in the rate law for the reaction is said to be order of a reaction.
The partial pressure of a gas in a mixture can be expressed as,
The ideal gas Law equation is,
Answer to Problem 13.132QP
Initial rate of the given reaction is
Explanation of Solution
Given,
Gas mixture containing
The elementary reaction is,
This reaction follows second order kinetics, with a rate constant of
Given mole fractions of
The initial rate of the reaction at
Rate law for the given reaction is,
Rate constant value for the given reaction is
Using mole fraction value and total partial pressure, partial pressure of each reactant in the reaction can be calculated as follows,
Molar concentration of reactants can be determined with the help of ideal gas equation,
Substitute the concentration and the rate constant into the rate law to find the initial rate of the reaction,
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