The rate constant k for a certain reaction is measured at two different temperatures: temperature 184.0 °C 249.0 °C OO E

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The Rate Constant K For A Certain Reaction Is Measured At Two Different Temperatures Temperature 184 0 C 249 0 C Oo E 1 (74.2 KiB) Viewed 60 times

The rate constant k for a certain reaction is measured at two different temperatures: temperature 184.0 °C 249.0 °C OO EXPLANATION Assuming the rate constant obeys the Arrhenius equation, calculate the activation energy E for this reaction. Round your answer to 2 significant digits. k 2.4×10¹1 x 10¹1 5.8 X The Arrhenius equation describes how the rate constant k of a reaction changes with temperature T: -E/RT In k = k = Ae In this equation, A stands for the pre-exponential or frequency factor, E stands for the activation energy, I stands for the absolute temperature, and R stands for the gas constant. An important fact about the Arrhenius equation is revealed by taking the natural logarithm of both sides: Ea 1 R T V = m x + ln A + b The natural log of the Arrhenius equation has the form of an equation of a line with slope m and y-intercept b.
What you see is that a graph of Ink versus 1/T will be a straight line with a slope of -E/R. By calculating the slope of the line that connects the two data points you're given, you can calculate E for the reaction. Here's how. a First, calculate Ink and 1/T for each point. Keep in mind that the I in the Arrhenius equation is the absolute temperature, measured in kelvins. 1/T temperature 184.0 °C 249.0 °C rise Ea Now calculate the slope of the line between the two points: A Ink (27.0863) (26.2039) A(1/T) Now set the slope equal to -E/R: Ea R E = R(3240.42 K) run k Ink 457.150 K 0.00218747 K 2.4 x 10¹¹ 26.2039 522.150 K 0.00191516 K¯¹5.8×10¹¹ 27.0863 = 8.31446 T = -3240.42 K 0.00191516 K E = 2.694 × 104 J mol K J mol −1 (3240.42 K) 0.00218747 K 1 -3240.42... K Here's the equality. Solve for Ea Substitute in the value of the gas constant R. Use the calculator.
Now set the slope equal to -E/R: a Ea R E = R(3240.42 K) = J E= € - (8.31446 ml) (324 = a K J mol E = 2.694 × 104 a - 3240.42 K E = 26.94 a EANSWER E = 27. a kJ mol (3240.42 K) kJ mol Don't forget to round your final answer to 2 significant digits. Here's the equality. Solve for E Substitute in the value of the gas constant R. Use the calculator. Convert to a more convenient prefixed unit.