Question

The rate constant for the decomposition of n2o5 is 7.78 × 10−7 at 273 k and 3.46 × 10−5 at t2. if the activation energy is 1027 kj/mol, what is the final temperature

Answer 1

The student's question about calculating the final temperature in a chemical reaction given the activation energy and rate constants at various temperatures requires the use of the Arrhenius equation, but cannot be completed without additional information such as the rate constant at the final temperature.

Step-by-step explanation:

The question relates to determining the final temperature for the decomposition of N2O5 when given an initial rate constant at 273 K, a rate constant at a second temperature, and the activation energy of 1027 kJ/mol. To find the final temperature, we use the Arrhenius equation, which shows the relationship between the rate constant, activation energy, and temperature. However, since the final temperature (T2) is not provided, we cannot calculate it with the given information. A complete question would need to provide either the rate constant at T2 or another piece of information allowing us to derive T2. The approach would involve rearranging the Arrhenius equation to solve for T2 and then applying logarithms and algebra to find its value.

Answer 2

Answer is: the temperature of the reaction is 275,48 K.
k₁ = 7,78·10⁻⁷ 1/s.

T₁ = 273 K.

Ea = 1027 kJ/mol = 1027000 J/mol.

k₂ = 3,46·10⁻⁵ 1/s.

R = 8,314 J/K·mol.
T₂ = ?
Natural logarithm of Arrhenius' equation:
lnk₁ = lnA - Ea/RT₁.
lnk₂ = lnA - Ea/RT₂.
ln(k₂/k₁) = (Ea/R) · (1/T₁ - 1/T₂).
ln(3,46·10⁻⁵ 1/s / 7,78·10⁻⁷ 1/s.) = (1027000 J/mol ÷ 8,314 J/K·mol) · ·(1/273K - 1/T₂).
3,79 = 123526,58 K · (0,00366 1/K - 1/T₂).
3,79 = 452,47 - 123526,58 · (1/T₂).
1/T₂ = 0,00363.
T₂ = 275,48 K.