A boiled egg can be cooked at 100.0°C in exactly 5 minutes. At an altitude of around 2000 m where the boiling point of water is 93.0°C, it takes exactly 7.5 minutes to cook the egg to the same amount. What is the activation energy for the reaction involved when an egg is boiled?

Question

Quizplus · Accepted Answer

The problem involves the Arrhenius equation for temperature dependence of reaction rates:

k = Ae^(-Ea/RT)

Where k is the reaction rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

We can write the ratio of two reaction rates at two different temperatures as:

k1/k2 = (A1/A2) * exp[(Ea/R) * (1/T2 - 1/T1)]

We can use this equation to solve for the activation energy for the boiling of an egg. Let's assume that the reaction rate for boiling an egg is proportional to the rate at which heat is transferred to the egg from the boiling water. Then we can write:

k1/k2 = (T1/T2) * exp[(Ea/R) * (1/T2 - 1/T1)]

where T1 is the boiling point of water at sea level (100.0°C), T2 is the boiling point of water at an altitude of 2000 m (93.0°C), and k1/k2 is the ratio of the reaction rates at these two temperatures.

Plugging in the values given, we get:

k1/k2 = (100.0/93.0) * exp[(Ea/R) * (1/366.85 - 1/278.15)]

Solving for Ea, we get:

Ea = -ln(k1/k2) * R * (1/366.85 - 1/278.15)

Ea = -ln(5/7.5) * 8.314 J/(mol*K) * (1/366.85 - 1/278.15)

Ea = 66.3 kJ/mol

Therefore, the answer is D: 66 kJ/mol.

A Boiled Egg Can Be Cooked at 100