A particular first-order reaction has a rate constant of 1.35 x 102s-1 at 25 deg

ID: 831944 • Letter: A

Question

A particular first-order reaction has a rate constant of 1.35 x 102s-1 at 25 degrees C. What is the magnitude of k at 75 degrees C if Ea = 85.6 kJ/mol?

A. 670 s-1
B. 3.47 x 104 s-1
C. 1.93 x 104 s-1
D. 3.85 x 106 s-1
E. 1.36 x 102 s-1"

I know the answer: but

K' / K = 10 2.155 = 143.05 how he coud get 143.05 and what is 10? and did he multebly or devide?

the answe is
According to Arrehenius Equation , K = A e -Ea / RT

Where

K = rate constant

T = temterature

R = gas constant = 8.314 J/mol-K

Ea = activation energy

A = Frequency factor(constant)

rate constant , K = A e - Ea/ RT

log K = log A - ( Ea / 2.303RT ) ---(1)

If we take rate constants at two different temperatures , then

log K = log A - ( Ea / 2.303RT ) --- (2)

& log K' = log A - ( Ea / 2.303RT' ) ---- ( 3)

Eq ( 3 ) - Eq ( 2 ) gives

log ( K' / K ) = ( Ea / 2.303 R ) x [ ( 1/ T ) - ( 1 / T' ) ]

Given

K = 1.35 x 102s-1

T = 25 degrees C = 25 + 273 = 298 K

K' = ?

T' = 75 degrees C = 75 + 273 = 348 K

Ea = 85.6 kJ/mol

= 85.6 x 1000 J/mol

Plug the values we get log ( K' / K ) = (85600/ 2.303x 8.314 ) x [ ( 1/298 ) - ( 1 / 348 ) ]

= 2.155

K' / K = 10 2.155

= 143.05

K' = 143.05 x 1.35 x 102 s-1

= 1.93 x 10 4 s-1

Explanation / Answer

According to Arrehenius Equation , K = A e -Ea / RT