Question

A) For the gas phase decomposition of hydrogen iodide at 700 K 2 HIH2 + I2 the average rate of disappearance of HI over the time period from t = 0 s to t = 1446 s is found to be 5.67×10-4 M s-1. The average rate of formation of H2 over the same time period is M s-1.

B) The rearrangement of cyclopropane to propene at 500 °C (CH2)3CH3CH=CH2 is first order in (CH2)3 with a rate constant of 6.70×10-4 s-1. If the initial concentration of (CH2)3 is 6.00×10-2 M, the concentration of (CH2)3 will be 1.06×10-2 M after s have passed.

C) The activation energy for the gas phase decomposition of ethyl chloroformate is 123 kJ. ClCOOC2H5C2H5Cl + CO2 The rate constant at 450 K is 2.62×10-4 /s. The rate constant will be 2.86×10-3 /s at K.

Answer 1

A) For the gas phase decomposition of hydrogen iodide at 700 K 2 HIH2 + I2 the average rate of disappearance of HI over the time period from t = 0 s to t = 1446 s is found to be 5.67×10-4 M s-1. The average rate of formation of H2 over the same time period is M s-1.

2 HI    ==> H2 + I2

we have, Rate of reaction = -1/2 d[HI]/dt = d[H2]/dt

since,   - d[HI]/dt = 5.67*10-4 M s-1

thus rate of reaction : 2.84*10-4 M s-1

thus, d[H2]/dt = 2.84*10-4 M s-1

B) The rearrangement of cyclopropane to propene at 500 °C (CH2)3CH3CH=CH2 is first order in (CH2)3 with a rate constant of 6.70×10-4 s-1. If the initial concentration of (CH2)3 is 6.00×10-2 M, the concentration of (CH2)3 will be 1.06×10-2 M after s have passed.

(CH₂)₃     ==> CH₃CH=CH₂

we have, k = 6.70×10-4 s-1

for first order reaction, k =1/t *ln {[A]₀ /[A]_t}

so, at that conc. of cyclo-propane , t = 1/k *ln {[A]₀ /[A]_t}

t = 1/(6.70×10-4 s-1) *ln {6.00×10-2 M /1.06×10-2 M}

t = 2587.3 sec.

C) The activation energy for the gas phase decomposition of ethyl chloroformate is 123 kJ. ClCOOC2H5C2H5Cl + CO2 The rate constant at 450 K is 2.62×10-4 /s. The rate constant will be 2.86×10-3 /s at K.

Ea = 123 kJ/mol

k (450) = 2.62×10-4 /s

k (T) = 2.86×10-3 /s

we have, k =   A exp.( -Ea /RT)

k(T) / k(450 K) = ( 2.86×10-3 /s / 2.62×10-4 /s) = 10.9

we have ,   exp.( -123*1000 J/mol /RT) / exp.( -123*1000 J/mol /R*450 K) = 10.9

or   exp.( -123*1000 J/mol /RT) = 5.75*10^-14

T = 485 K