Chem question on rate constant.?

Question

NO(g) + O3 (g) ? NO2(g) + O2(g)

The rate constant at 25o C is 1.9 x 1010M-1s-1 and the value for Ea/R is 2.450 x 103 K.

What is the value of the rate constant at -40o C?

Answer 1

Use Arrhenius equation:

k = A·exp{- Ea/(R·T)}

Knowing the rate constant k₀ for one certain temperature T₀, you can determine the collision factor A:

k₀ = A·exp{- Ea/(R·T₀)}

<=>

A = k₀ / exp{- Ea/(R·T₀)}

substitute this expression to the general equation:

k = k₀·exp{- Ea/(R·T)}/exp{- Ea/(R·T₀)}

= k₀·exp{- (Ea/R)·(1/T - 1/T₀)}

So for

T₀ = 25°C = 298K and T = -40°C = 233K

k = 1.9×10¹⁰M⁻¹s⁻¹ · exp{- 2.45×10³·(1/233K - 1/298K)}

= 1.9×10⁹M⁻¹s⁻¹