Chemistry Practice Problems Arrhenius Equation Practice Problems Solution: A first-order reaction has rate constants of 4.6 x...

Solution: A first-order reaction has rate constants of 4.6 x 10 -2 s-1 and 8.1 x 10-2 s-1 at 0°C and 20.°C, respectively. What is the value of the activation energy?

Problem

A first-order reaction has rate constants of 4.6 x 10 -2 s-1 and 8.1 x 10-2 s-1 at 0°C and 20.°C, respectively. What is the value of the activation energy?

Solution

The rate constant of a chemical reaction is a temperature dependent quantity.


The relation between the rate constant and temperature is quantified by the Arrhenius equation.


<math xmlns="http://www.w3.org/1998/Math/MathML"><menclose mathcolor="#0000FF" notation="box"><mi>ln</mi><mfenced><mfrac><msub><mi>k</mi><mn>2</mn></msub><msub><mi>k</mi><mn>1</mn></msub></mfrac></mfenced><mo>&#xA0;</mo><mo>=</mo><mfrac><mrow><mo>&#xA0;</mo><mo>-</mo><msub><mi>E</mi><mi>a</mi></msub></mrow><mi>R</mi></mfrac><mfenced><mrow><mfrac><mn>1</mn><msub><mi>T</mi><mn>2</mn></msub></mfrac><mo>-</mo><mfrac><mn>1</mn><msub><mi>T</mi><mn>1</mn></msub></mfrac></mrow></mfenced></menclose></math>


We have the following data:


k1 = 4.6x10-2 s-1 at T1 = 0 oC

k2 = 8.1x10-2 s-1 20 °C

R = 8.314 J/mol/K

Ea = ?


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