Answer : The rate constant will increase by a factor of 7.5
Explanation :
The relationship between Temperature and rate constant can be explained with the help of Arrhenius equation. The equation is given below.
㏑ (k₂/k₁) = - Ea/R ( 1/T₂ - 1/T₁)
Here k₁ & k₂ represent rate constants at temperatures T₁ and T₂
The temperature is expressed in Kelvin unit
Ea is activation energy which is expressed in J/mol
R is gas constant which is 8.314 J mol⁻¹ K⁻¹
Here we know that T₁ is initial temperature which is 200° C
To convert Celsius to Kelvin we add 273
Therefore T₁ = 200 + 273 = 473 K
T₂ = 220 + 273 = 493 K
Ea = 195 kJ/mol . We will convert kJ to J
The conversion factor is 1 kJ = 1000 J
195 kJ × (1000 J / 1 kJ) = 195000 J
So Ea = 195000 J
Let us plug in these values in Arrhenius equation now.
ln k₂/k₁ = - 195000 J mol⁻¹ / 8.314 J mol⁻¹ K⁻¹ ( 1/493 K - 1/473 K)
ln k₂/k₁ = - 23454.4 ( 0.0020284 - 0.0021142)
ln k₂/k₁ = -23454.4 × ( -8.58 × 10⁻⁵)
ln k₂/k₁ = 2.012
k₂/k₁ = e^ (2.012)
k₂/k₁ = 7.48
The above answer can be rounded to 7.5
Therefore we have k₂/k₁ = 7.5
k₂ = 7.5 k₁
We know that k₂ is the rate constant at 220° C and k₁ is the rate constant at 200°C.
Therefore we can say that the rate constant will increase by a factor of 7.5
