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The rate constant of a chemical reaction increased from 0.100 s−1 to 3.10 s−1 upon raising the temperature from 25.0 ∘C to 51.0 ∘C .

Part A

Calculate the value of (1/T2−1/T1) where T1 is the initial temperature and T2 is the final temperature.

Express your answer numerically.

Part B

Calculate the value of ln(k1/k2) where k1 and k2 correspond to the rate constants at the initial and the final temperatures as defined in part A.

Express your answer numerically.

Part C

What is the activation energy of the reaction?

Express your answer numerically in kilojoules per mole.

Respuesta :

hamzaahmeds

Answer:

A. (1/T₂ - 1/T₁) = -2.69 x 10⁻⁴ K⁻¹

B. ln (k₁/k₂) = -3.434

C. E = 106.13 KJ/mol

Explanation:

Part A:

we have:

T₁ = 25°C = 298 K

T₂ = 51°C = 324 K

(1/T₂ - 1/T₁) = (1/324 k - 1/298 k)

(1/T₂ - 1/T₁) = -2.69 x 10⁻⁴ K⁻¹

Part B:

ln (k₁/k₂) = ln (0.1/3.1)

ln (k₁/k₂) = -3.434

Part C:

The activation energy can be found out by using Arrhenius Equation:

ln (k₁/k₂) = E/R  (1/T₂ - 1/T₁)

where,

E = Activation Energy

R = General Gas Constant = 8.314 J/mol.k

Therefore,

-3.434 = (E/8.314 J/mol.k)(-2.69 x 10⁻⁴ K⁻¹)

E = 106134.8 J/mol = 106.13 KJ/mol

Part A. (1/T₂ - 1/T₁) = -2.69 x 10⁻⁴ K⁻¹

Part B. ln (k₁/k₂) = -3.434

Part C. E = 106.13 KJ/mol

Calculation of Initial temperature

Part A:

we have this information:

T₁ is = 25°C = 298 K

Then T₂ = 51°C = 324 K

After that (1/T₂ - 1/T₁) = (1/324 k - 1/298 k)

Therefore, (1/T₂ - 1/T₁) = -2.69 x 10⁻⁴ K⁻¹

Part B:

ln (k₁/k₂) is = ln (0.1/3.1)

ln (k₁/k₂) is = -3.434

Part C:

When The activation energy can be found by using Arrhenius Equation are:

ln (k₁/k₂) is = E/R (1/T₂ - 1/T₁)

where is,

E is = Activation Energy

Then R = General Gas Constant = 8.314 J/mol.k

Now, -3.434 = (E/8.314 J/mol.k)(-2.69 x 10⁻⁴ K⁻¹)

Therefore, E = 106134.8 J/mol = 106.13 KJ/mol

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