calculate the rate constant at 225C for a reaction that has a rate constant of 8.1X10^-4 at 95c and an activation enegry of 93.0 kj/mol
So glad he told me to use the arrhenius equation. because i had ABSOLUTELY NO FREAKING IDEA TO TRY THAT BEFORE I CAME TO THIS PAGE. if you are going to comment with advice, try and think a little about your post before you post it.
To calculate the rate constant at 225°C for a reaction, we can use the Arrhenius equation:
k2 = k1 * exp((Ea / R) * ((1/T2) - (1/T1)))
Where:
k2 is the rate constant at 225°C
k1 is the rate constant at 95°C (8.1 × 10^-4)
Ea is the activation energy (93.0 kJ/mol)
R is the universal gas constant (8.314 J/mol·K)
T2 is the temperature in Kelvin at 225°C (225 + 273 = 498 K)
T1 is the temperature in Kelvin at 95°C (95 + 273 = 368 K)
Let's substitute these values into the equation and calculate k2:
k2 = (8.1 × 10^-4) * exp((93.0 / 8.314) * ((1/498) - (1/368)))
First, let's calculate the exponential term:
exp((93.0 / 8.314) * ((1/498) - (1/368))) ≈ exp((93.0 / 8.314) * (0.002008 - 0.002717)) ≈ exp((93.0 / 8.314) * (-0.000709)) ≈ exp(-0.796)
Now, we can substitute this value into the equation:
k2 ≈ (8.1 × 10^-4) * exp(-0.796)
Using a calculator, we find that exp(-0.796) ≈ 0.4500 (rounded to four decimal places). Let's continue the calculation:
k2 ≈ (8.1 × 10^-4) * 0.4500 ≈ 3.645 × 10^-4
Therefore, the rate constant at 225°C is approximately 3.645 × 10^-4.
To calculate the rate constant at 225°C for a reaction, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) to the temperature (T) and the activation energy (Ea):
k = A * e^(-Ea / (R * T))
Where:
- k is the rate constant
- A is the pre-exponential factor or frequency factor
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol*K))
- T is the temperature (in Kelvin)
We are given the following information:
- The rate constant (k) at 95°C is 8.1 x 10^-4.
- The activation energy (Ea) is 93.0 kJ/mol.
First, we need to convert the temperatures from Celsius to Kelvin. To do this, we add 273.15 to each temperature:
95°C + 273.15 = 368.15 K
225°C + 273.15 = 498.15 K
Now, we can plug in the values into the Arrhenius equation to solve for the rate constant at 225°C:
k2 = A * e^(-Ea / (R * T2))
k2 = 8.1 x 10^-4 * e^(-93.0 kJ/mol / (8.314 J/(mol*K) * 498.15 K))
k2 = 8.1 x 10^-4 * e^(-93000 J/(mol) / (4151.89 J/(mol*K)))
k2 = 8.1 x 10^-4 * e^(-22.38)
k2 ≈ 8.1 x 10^-4 * 2.95 x 10^-10
k2 ≈ 2.39 x 10^-13
Therefore, the rate constant at 225°C is approximately 2.39 x 10^-13.