Question

1) The speed constant was determined for the first order decomposition of an organic compound at various temperatures:

Calculate the activation energy for the reaction. Build a graph of Arhenius

2) The hydrolysis of sucrose. in which a sucrose molecule is broken in a glucose molecule and a fructose molecule, is part of the digestive process. Calculate the speed constant for the hydrolysis of sucrose at 35,0 C knowing that k=1,0x10^-3 L mol^-1s^-1 at 37 C and that the activation energy is 108kj mol^-1

Answer 1

1) Eₐ = 100.3 kJ/mol

2) k = 7.62×10⁻⁴ M⁻¹s⁻¹

Step-by-step explanation:

1) Make an Arrhenius graph by plotting ln(k) on the y-axis and 1/T on the x-axis (don't forget to convert temperature to Kelvin).

The slope of the line is equal to -Eₐ/R.

-Eₐ/R = -12065

Eₐ = 100,300 J/mol

Eₐ = 100.3 kJ/mol

2) Since we know the slope of ln(k) vs 1/T is -Eₐ/R, we can say:

-Eₐ/R = (ln(k₂) − ln(k₁)) / (1/T₂ − 1/T₁)

Plug in values and solve for k:

-(108,000 J/mol) / (8.314 J/mol/K) = [ln(k) − ln(1.0×10⁻³)] / [1/(35+273.15 K) − 1/(37+273.15 K)]

-12990 = [ln(k) + 6.91] / (2.09×10⁻⁵ K⁻¹)

-0.272 = ln(k) + 6.91

ln(k) = -7.18

k = 7.62×10⁻⁴ M⁻¹s⁻¹