Areaction has an activation energy of 195.0 kj/mol. when the temperature is increased from 200. °c to 220.°c, the rate constant will increase by a factor of

The rate constant will increase by a factor of 6.5.

Using the Arrhenius equation;

ln(k2/k1) = -Ea/R(1/T2 - 1/T1)

k1 = rate constant at 200. °c

k2 = rate constant at 220.°c

Ea = Activation energy

T2 =  220.°c or 493 K

T1 = 200. °c or 473 K

Hence;

ln(k2/k1) = -195.0 × 10^3/8.314(1/493 - 1/473)

k2/k1 = 6.5

Hence;

k2 = 6.5k1

The rate constant will increase by a factor of 6.5.

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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