The rate constants for a first order decay reaction are found to be:
K287.3C = 1 X 10-4s-1
K327.4C = 19.2 X 10-4s-1
(a) Determine the value, in s-1 of K250C
(b) How long will it take, at 350C, for the reactant to decay to 1% of its original concentration? Express your answer in seconds.
a)4.27 x 10^-6
b) 536.7
a) 4.27 x 10^-6
b) 536.7
To determine the value of K250C, we can use the Arrhenius equation, which relates the rate constant to temperature.
The Arrhenius equation is given by:
K = A * exp(-Ea / (RT))
Where:
K = rate constant
A = pre-exponential factor (also known as frequency factor or Arrhenius factor)
Ea = activation energy
R = ideal gas constant (8.314 J/(mol K))
T = temperature in Kelvin
To find the value of K250C, we need to determine the activation energy (Ea), pre-exponential factor (A), and the temperature (T) for both K287.3C and K327.4C.
Given:
K287.3C = 1 × 10^-4 s^-1
K327.4C = 19.2 × 10^-4 s^-1
To determine the value of K250C, we can use the following steps:
1. Convert 287.3°C and 327.4°C to Kelvin by adding 273.15 to each temperature:
T287.3C = 287.3 + 273.15 = 560.45 K
T327.4C = 327.4 + 273.15 = 600.55 K
2. Use the Arrhenius equation with the known rate constants and temperatures to solve for the activation energy (Ea) and pre-exponential factor (A) of the reaction.
For K287.3C:
1 × 10^-4 s^-1 = A * exp(-Ea / (8.314 J/(mol K) * 560.45 K))
For K327.4C:
19.2 × 10^-4 s^-1 = A * exp(-Ea / (8.314 J/(mol K) * 600.55 K))
By solving the two equations simultaneously, we can find the values of Ea and A.
Once we have the values of Ea and A, we can use the Arrhenius equation with the new temperature, T250C, to find the value of K250C.
(b) To find the time it takes for the reactant to decay to 1% of its original concentration at 350°C, we can use the first-order decay equation:
ln(Ct / C0) = -kt
Where:
Ct = final concentration of the reactant
C0 = initial concentration of the reactant
k = rate constant
t = time
In this case, Ct is 1% of C0, so Ct / C0 = 0.01.
We can rearrange the equation to solve for t:
t = -ln(0.01) / k
Plug in the given rate constant at 350°C and calculate the time t.