1)At room temperature (20 degree C), milk turns sour in about 64 hours. In a refrigerator at 3 degree C, milk can be stored three times as long before it sours. How long should it take milk to sour at 40 degree C (activation energy =44kj/mol)?

2)At what temperature will the rate constant for the reaction H2(g)+I(g) -> 2HI(g) have the value 5.3¡¿10^−3 /Ms? (Assume k=5.4*10^-4/Ms at 599 and k=2.8*10^-2/Ms at 683 .)

200

1) To solve this question, we can use the Arrhenius equation to determine the rate constant for the souring of milk at 40 degrees Celsius.

The Arrhenius equation is given by:
k = A * exp(-Ea / (R * T))

Where:
k is the rate constant,
A is the pre-exponential factor,
Ea is the activation energy,
R is the gas constant (8.314 J/(mol*K)),
T is the temperature in Kelvin.

First, we need to convert the activation energy from kilojoules to joules:
Ea = 44 kJ/mol * 1000 J/kJ = 44000 J/mol

Next, let's convert the temperatures to Kelvin:
20 degrees Celsius + 273.15 = 293.15 K
3 degrees Celsius + 273.15 = 276.15 K

Now, let's calculate the rate constant at 3 degrees Celsius:
k_3 = A * exp(-44000 J/mol / (8.314 J/(mol*K) * 276.15 K))

Since we know that milk can be stored three times as long at 3 degrees Celsius compared to room temperature, the rate constant at room temperature (20 degrees Celsius) would be three times higher:
k_20 = 3 * k_3

Finally, we can calculate the rate constant at 40 degrees Celsius using the same logic:
k_40 = (k_20 / 3) * exp(-44000 J/mol / (8.314 J/(mol*K) * 313.15 K))

So, the rate constant at 40 degrees Celsius can be determined using the above equation.

2) To solve this question, we can use the Arrhenius equation again to determine the temperature at which the rate constant for the given reaction has a specific value.

Using the Arrhenius equation:
k = A * exp(-Ea / (R * T))

Let's assume that the pre-exponential factor (A) remains constant.

At temperature T1 = 599 K, we have k_1 = 5.4 * 10^-4 /Ms
At temperature T2 = 683 K, we have k_2 = 2.8 * 10^-2 /Ms

We can write two equations using the Arrhenius equation for these two temperatures:
k_1 = A * exp(-Ea / (8.314 J/(mol*K) * 599 K))
k_2 = A * exp(-Ea / (8.314 J/(mol*K) * 683 K))

Dividing these two equations:
k_1 / k_2 = exp(-Ea / (8.314 J/(mol*K)) * (599 K - 683 K))

Now, we can solve for the temperature at which k has the desired value:
T = [(Ea / (8.314 J/(mol*K)) * (599 K - 683 K)) / ln(k_1 / k_2)]

By substituting the known values for k_1, k_2, Ea, and the gas constant R, you can calculate the temperature T at which the rate constant has the desired value.