The time for which the oxygen atom remains adsorbed on a tungsten surface is 0.36 at 2550 K and 3.49 at2360 K. Calculate the activation energy of desorption of oxygen atom.a)490 kJ/molb)550 kJ/molc)690.3 kJ/mold)598.2 kJ/molCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Given:
Time for which oxygen atom remains adsorbed on tungsten surface at 2550 K, t1 = 0.36 s
Time for which oxygen atom remains adsorbed on tungsten surface at 2360 K, t2 = 3.49 s

To find: Activation energy of desorption of oxygen atom

Formula:
The rate constant for desorption of oxygen atom can be calculated using the Arrhenius equation:
k = A * exp(-Ea/RT)

Where:
k = rate constant
A = pre-exponential factor
Ea = activation energy
R = gas constant (8.314 J/mol·K)
T = temperature (K)

Calculation:
We can use the Arrhenius equation to find the activation energy of desorption of oxygen atom.
Taking the natural logarithm of both sides of the equation, we get:
ln(k) = ln(A) - (Ea/RT)

We can rewrite this equation as:
ln(k1) = ln(A) - (Ea/R) * (1/T1)
ln(k2) = ln(A) - (Ea/R) * (1/T2)

Subtracting the second equation from the first equation, we get:
ln(k1) - ln(k2) = (Ea/R) * (1/T2 - 1/T1)

We know that ln(a) - ln(b) = ln(a/b), so we can rewrite the equation as:
ln(k1/k2) = (Ea/R) * (1/T2 - 1/T1)

Rearranging the equation to solve for Ea, we get:
Ea = -R * ln(k1/k2) / (1/T2 - 1/T1)

Plugging in the given values, we have:
Ea = -8.314 J/mol·K * ln(0.36/3.49) / (1/2360 K - 1/2550 K)

Converting the units of Ea from J/mol to kJ/mol, we get:
Ea = -8.314 * 10^-3 kJ/mol·K * ln(0.36/3.49) / (1/2360 K - 1/2550 K)

Evaluating the expression, we find:
Ea ≈ 598.2 kJ/mol

Therefore, the activation energy of desorption of oxygen atom is approximately 598.2 kJ/mol. Hence, option 'D' is the correct answer.

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