The reaction between nitrogen dioxide and carbon monoxide isNO2 (g) + CO (g) →NO (g) + CO2 (g) The rate constant at 701 K is measured as 2.57 M-1⋅s-1 and that at 895 K is measured as 567 M-1⋅s-1. The activation energy is 1.5*102 kJ/mol. Predict the rate constant at 525 K. Express the rate constant in liters per mole-second to three significant figures.

Question

Adam Sweeney

Chemistry

12 January, 06:07

The reaction between nitrogen dioxide and carbon monoxide isNO2 (g) + CO (g) →NO (g) + CO2 (g) The rate constant at 701 K is measured as 2.57 M-1⋅s-1 and that at 895 K is measured as 567 M-1⋅s-1. The activation energy is 1.5*102 kJ/mol. Predict the rate constant at 525 K. Express the rate constant in liters per mole-second to three significant figures.

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Adrian Salas · Answer 1

Given data

K1 = 2.57 M-1s-1

T1 = 701 K

K2=?

T2 = 525 K

Ea = 150 kJ / mol * 1000 J * / 1 kJ = 150000 J / mol

Formula to calculate the rate constant using the activation energy is as follows

ln[K2/K1] = (Ea / R) * [ (1/T1) - (1/T2) ]

where R = 8.314 J per mol. K

lets put the values in the formula and calculate the activation energy

ln [K2/2.57] = 150000 J per mol / 8.314 J per K. mol * [ (1/701) - (1/525) ]

ln [K2/2.57] = - 8.628

K2 / 2.57 = anti ln [-8.628]

K2/2.57 = 0.000179

K2 = 0.000179 * 2.57

K2 = 0.00046

Therefore rate constant at 525 K is 4.6*10^-4 L/mol. s