Don't know where to begin.
1) A thermally activated process (a reaction) takes four minutes at 811°C. How long will it take (in minutes) at 748°C if the activation energy is 150 kJ/mol?
Use the Arrhenius equation. Choose any concentration you wish but the easy number is 1.
k1 is 1/4
k2 = ?
T2 is 811 C converted to K.
T1 is 748 C converted to K.
Ea is 150,000
Post your work if you get stuck.
but that get with this?????
I don't understand. What does "but that get with this????" mean?
yes, that formula I use for this
It's the Arrhenius equation.
Substitute the numbers I gave in the earlier response and solve for k2.
the response must express it in minutes and I don't know where it will go out if what I get is a constant
I am grateful can collaborate me
To find out how long the reaction will take at a different temperature, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant of a chemical reaction to the temperature and the activation energy.
The Arrhenius equation is given by:
k = A * exp (-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor or the frequency factor, which represents the number of collisions happening in the correct orientation per unit time
- Ea is the activation energy
- R is the ideal gas constant (8.314 J/(mol*K))
- T is the temperature in Kelvin
Since we are given the time in minutes, we need to convert the temperature from Celsius to Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15.
So, for the given problem, let's break down the steps:
1) Convert the temperatures to Kelvin:
- 811°C + 273.15 = 1084.15 K (Temperature 1)
- 748°C + 273.15 = 1021.15K (Temperature 2)
2) Calculate the ratio of the rate constants:
k1/k2 = exp((Ea/R) * ((1/T2) - (1/T1)))
Let's plug in the values:
k1/k2 = exp((150,000 J/mol / (8.314 J/(mol*K)) * ((1/1021.15K) - (1/1084.15K)))
3) Solve for k2/k1:
k2/k1 = 1 / exp((150,000 J/mol / (8.314 J/(mol*K)) * ((1/1021.15K) - (1/1084.15K)))
4) Since the rate constant is inversely proportional to time, we can say:
t2/t1 = k1/k2
Solve for t2:
t2 = (t1 * k1) / k2
Now, substitute the given values:
t2 = (4 minutes * k1) / k2
5) Calculate k1 and k2:
k1 = k at T1 = 4 minutes
k2 = k at T2
6) Plug the values of k1 and k2 into the equation:
t2 = (4 minutes * k at T1) / k at T2
By following these steps, you should be able to calculate how long it will take for the reaction to proceed at 748°C.