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 rate of the reaction at this temperature.
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,
Want to see more full solutions like this?
Chapter 13 Solutions
Chemistry
- Gaseous azomethane (CH3N2CH3) decomposes to ethane and nitrogen when heated: CH3N2CH3(g) CH3CH3(g) + N2(g) The decomposition of azomethane is a first-order reaction with k = 3.6 104 s1 at 600 K. (a) A sample of gaseous CH3N2CH3 is placed in a flask and heated at 600 K for 150 seconds. What fraction of the initial sample remains after this time? (b) How long must a sample be heated so that 99% of the sample has decomposed?arrow_forwardGaseous azomethane, CH3N=NCH3, decomposes in a first-order reaction when heated: CH3N=NCH3(g) N2(g) + C2H6(g) The rate constant for this reaction at 600 K is 0.0216 min1. If the initial quantity of azomethane in the flask is 2.00 g, how much remains after 0.0500 hour? What mass of N2 is formed in this time?arrow_forwardThe reaction 2 NO(g) + 2 H2(g) N2(g) + 2 H2O(g) was studied at 904 C, and the data in the table were collected. (a) Determine the order of the reaction for each reactant. (b) Write the rate equation for the reaction. (c) Calculate the rate constant for the reaction. (d) Find the rate of appearance of N2 at the instant when [NO] = 0.350 mol/L and [H] = 0.205 mol/L.arrow_forward
- The decomposition of ozone is a second-order reaction with a rate constant of 30.6 atm1 s1 at 95 C. 2O3(g)3O2(g) If ozone is originally present at a partial pressure of 21 torr, calculate the length of time needed for the ozone pressure to decrease to 1.0 torr.arrow_forwardAt 573 K, gaseous NO2(g) decomposes, forming NO(g) and O2(g). If a vessel containing NO2(g) has an initial concentration of 1.9 102 mol/L, how long will it take for 75% of the NO2(g) to decompose? The decomposition of NO2(g) is second-order in the reactant and the rate constant for this reaction, at 573 K, is 1.1 L/mol s.arrow_forwardHydrogen peroxide, H2O2(aq), decomposes to H2O() and O2(g) in a reaction that is first-order in H2O2 and has a rate constant k = 1.06 103 min1 at a given temperature. (a) How long will it take for 15% of a sample of H2O2 to decompose? (b) How long will it take for 85% of the sample to decompose?arrow_forward
- Nitryl fluoride is an explosive compound that can be made by oxidizing nitrogen dioxide with fluorine: 2 NO2(g) + F2(g) → 2 NO2F(g) Several kinetics experiments, all done at the same temperature and involving formation of nitryl fluoride, are summarized in this table: Write the rate law for the reaction. Determine what the order of the reaction is with respect to each reactant and each product. Calculate the rate constant k and express it in appropriate units.arrow_forwardThe initial concentration of the reactant in a tirst-order reaction A —» products is 0.64 rnol/L and the half-life is 30.0 s. Calculate the concentration of the reactant exactly 60 s after initiation of the reaction. How long would it take for the concentration of the reactant to drop to one-eighth its initial value? How long would it take for the concentration of the reactant to drop to 0.040 mol/L?arrow_forwardThe Raschig reaction produces the industrially important reducing agent hydrazine, N2H4, from ammonia, NH3, and hypochlorite ion, OCl−, in basic aqueous solution. A proposed mechanism is Step 1: Step 2: Step 3: What is the overall stoichiometric equation? Which step is rate-limiting? What reaction intermediates are involved? What rate law is predicted by this mechanism?arrow_forward
- Chemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning
- Chemistry for Engineering StudentsChemistryISBN:9781285199023Author:Lawrence S. Brown, Tom HolmePublisher:Cengage LearningChemistry for Engineering StudentsChemistryISBN:9781337398909Author:Lawrence S. Brown, Tom HolmePublisher:Cengage LearningChemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage Learning