Textbook Question
The half-life for the radioactive decay of C-14 is 5715 years and is independent of the initial concentration. How long does it take for 25.00% of the C-14 atoms in a sample of C-14 to decay?
Ch.15 - Chemical Kinetics
Chapter 15, Problem 67
The activation energy of a reaction is 44.2 kJ/mol and the frequency factor is 1.9⨉1011/ s. Calculate the rate constant of the reaction at 25 °C.
Verified step by step guidance1
Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius.
Use the Arrhenius equation: k = A * e^(-Ea/(R*T)), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant (8.314 J/mol*K), and T is the temperature in Kelvin.
Convert the activation energy from kJ/mol to J/mol by multiplying by 1000.
Substitute the values for A, Ea, R, and T into the Arrhenius equation.
Calculate the exponent and then the rate constant k using the Arrhenius equation.
Verified Solution
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Activation Energy
Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. In the context of the Arrhenius equation, a higher activation energy typically results in a slower reaction rate, as fewer molecules have sufficient energy to react at a given temperature.
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02:02
Activity Series Chart
Arrhenius Equation
The Arrhenius equation relates the rate constant of a reaction to its activation energy and temperature. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation allows for the calculation of the rate constant based on the energy dynamics of the reaction.
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01:20Arrhenius Equation
Temperature Conversion
In chemical calculations, temperatures must often be converted to Kelvin, as the Kelvin scale is the standard for thermodynamic equations. To convert Celsius to Kelvin, one adds 273.15 to the Celsius temperature. For example, 25 °C is equivalent to 298.15 K. Accurate temperature conversion is crucial for correctly applying the Arrhenius equation and determining the rate constant.
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02:10Temperature Conversion Example
Related Practice
Textbook Question
The half-life for the radioactive decay of C-14 is 5715 years and is independent of the initial concentration. If a sample of C-14 initially contains 1.5 mmol of C-14, how many millimoles are left after 2725 years?
Textbook Question
The diagram shows the energy of a reaction as the reaction progresses. Label each blank box in the diagram.
a. reactants b. products c. activation energy (Ea) d. enthalpy of reaction (ΔHrxn)
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Textbook Question
The rate constant (k) for a reaction was measured as a function of temperature. A plot of ln k versus 1/T (in K) is linear and has a slope of -7012 K. Calculate the activation energy for the reaction.
Textbook Question
The data shown here were collected for the first-order reaction: N2O(g) → N2(g) + O(g) Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.
Temperature (K) Rate Constant (1 , s)
800 3.24⨉10- 5
900 0.00214
1000 0.0614
1100 0.955
1575
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Textbook Question
The tabulated data show the rate constant of a reaction measured at several different temperatures. Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.
Temperature (K) Rate Constant (1 , s)
300 0.0134
310 0.0407
320 0.114
330 0.303
340 0.757
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