The reaction,
C2H5Br --> C2H4 + HBr,
has a rate constant k = 0.0000100 s-1 at 363 °C and k = 0.000479 s-1 at 427 °C. What is the rate constant for the reaction at 725 K? Round your answer to 3 significant figures.
I would use the Arrhenius equation along with k @ 363 C and k @ 427 C (remember to change those to Kelvin) to calculate activation energy and use that activation energy with the k @ 427C to calculate the new k @ 725 K.
so...
k=Ae^(Ea/RT)
Do I set it up as ratios? I.e.
0.0000100s-1=Ae^(-Ea/R * 636)
____________________________
0.000479s-1=Ae^(-Ea/R * 700)
A cancels out
...and then solve from there?
I would use the integrated form. I use
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)
oooh, righteous! Thanks so much I appreciate the time you take out to help!
To find the rate constant for the reaction at 725 K, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) to the activation energy (Ea) and the temperature (T). The equation is given as:
k = A * e^(-Ea/RT),
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.
Given the rate constants at 363 °C and 427 °C, we need to convert these temperatures to Kelvin before we can use the Arrhenius equation. The conversion formula is:
T(K) = T(°C) + 273.15,
Using this formula, we have:
- T1 = 363 °C + 273.15 = 636.15 K,
- T2 = 427 °C + 273.15 = 700.15 K.
Now we can use the Arrhenius equation to solve for the values of A and Ea. We'll use the two sets of temperature and rate constant values to create two separate equations:
1) k1 = A * e^(-Ea/RT1),
2) k2 = A * e^(-Ea/RT2).
Dividing equation (2) by equation (1) eliminates A, which allows us to solve for Ea:
k2/k1 = (A * e^(-Ea/RT2))/(A * e^(-Ea/RT1)),
k2/k1 = e^(-Ea/RT2 + Ea/RT1).
Taking the natural logarithm of both sides gives:
ln(k2/k1) = -Ea/R * (1/T2 - 1/T1).
Now we can rearrange the equation to solve for Ea:
Ea = -R * (ln(k2/k1))/(1/T2 - 1/T1).
Plugging in the given values of k1, T1, k2, and T2 will allow us to calculate Ea.
Once we have Ea, we can use the Arrhenius equation with the desired temperature of 725 K to find the rate constant k for the reaction at that temperature.