IF a reation generally takes 40 seconds to occur at 45 degrees C, how long should the reaction take a t the following temperatures?
A. 35C
B. 55C
C. 65C
The rule of thumb, which is not exact, is that the reaction doubles for every 10 C rise in temperature. So at 35 it should be 1/2, at 55 should be double, and at 65 should be doubled again (4x)
the lower the temperture the longer it should take correct?
yes.
ok so
A.20 seconds
B. 80 seconds
C. 120 seconds
20 is ok
80 is ok
If you double again, that is 160 seconds. Or double x double = 4x and 4 x 40 = 160
Thank You
To determine the time required for the reaction to occur at different temperatures, we can use the Arrhenius equation, which relates the rate constant of a reaction to the temperature.
The Arrhenius equation is given by:
k = Ae^(-Ea/RT)
Where:
k is the rate constant
A is the pre-exponential factor (a constant)
Ea is the activation energy
R is the ideal gas constant (8.314 J/(mol·K))
T is the absolute temperature in Kelvin
First, we need to convert the given temperatures from Celsius to Kelvin by adding 273.15 to each temperature.
A. For 35°C:
T = 35°C + 273.15 = 308.15 K
B. For 55°C:
T = 55°C + 273.15 = 328.15 K
C. For 65°C:
T = 65°C + 273.15 = 338.15 K
Now, let's calculate the ratio of the rate constants at different temperatures using the Arrhenius equation:
k1 = A * e^(-Ea/(R*T1)) [k1 represents the rate constant at 45°C]
k2 = A * e^(-Ea/(R*T2)) [k2 represents the rate constant at the given temperature]
To find the time required for the reaction at each temperature, we can compare the rate constants:
t2 = (k1 * t1) / k2
Where:
t1 is the time taken at 45°C (40 seconds)
t2 is the time required at the given temperature
k1 is the rate constant at 45°C
k2 is the rate constant at the given temperature
By substituting the values into the equation for each temperature, we can calculate the time required:
A. For 35°C:
k2 = A * e^(-Ea/(R*T2))
t2 = (k1 * t1) / k2
B. For 55°C:
k2 = A * e^(-Ea/(R*T2))
t2 = (k1 * t1) / k2
C. For 65°C:
k2 = A * e^(-Ea/(R*T2))
t2 = (k1 * t1) / k2
Please provide the values of A and Ea (pre-exponential factor and activation energy) to proceed with the calculation.