Question

The following data show the rate constant of a reaction measured at several different temperatures. Temperature (K) Rate Constant (1/s) 310 0.194 320 0.554 330 1.48 340 3.74 350 8.97 Part APart complete Use an Arrhenius plot to determine the activation barrier for the reaction. Express your answer using three significant figures. Ea

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

Part A

    activation barrier for the reaction $E_a = 84 .0 \ KJ/mol$

Part B

    The frequency plot is  $A = 2.4*10^{13} s^{-1}$    

Explanation:

From the question we are told that

     at  $T_1 = 300 \ K$   $k_1 = 5.70 *10^{-2}$

and  at  $T_2 = 310 \ K$   $k_2 = 0.169$

The  Arrhenius plot is mathematically represented as

      $ln [\frac{k_2}{k_1} ] = \frac{E_a}{R} [\frac{1}{T_1} - \frac{1}{T_2} ]$

Where $E_a$ is the activation barrier for the reaction

         R is the gas constant with a value of  $R = 8.314*10^{-3} KJ/mol \cdot K$

Substituting values

          $ln [\frac{0.169}{6*10^-2{}} ] = \frac{E_a}{8.314*10^{-3}} [\frac{1}{300} - \frac{1}{310} ]$

=>       $E_a = 84 .0 \ KJ/mol$

The  Arrhenius plot can also be  mathematically represented as

      $k = A * e^{-\frac{E_a}{RT} }$

Here we can use any value of k from the data table with there corresponding temperature let take  $k_2 \ and \ T_2$

So substituting values

        $0.169 = A e ^{- \frac{84.0}{8.314*10^{-3} * 310} }$

=>       $A = 2.4*10^{13} s^{-1}$