A reaction rate doubles when the temperature increases from 0 degrees Celsius to 10 degrees Celsius, maintaining everything else equal. What is the activation energy for this reaction? (R = 8.314 J/mol K)
Hey Walter, for this we use the arrhenius equation:
In(K2/K1)= -Ea/R (1/T2-1/T1)
As it says the reaction rate doubles. so for instance if you take K1= 1 then K2 will equal to 2. Now plug this into In(K2/K1)= -Ea/R (1/T2-1/T1)
Now after we do In(K2/K1)= 0.693
0.693=-Ea/R (1/T2 - 1/T1). Now we have to get -Ea by itself.
0.693 X (8.314)/ (1/T1-1/T2)= -Ea
5.763/ (1/T2 -1/T1) = -Ea
5.763/ (1/(273+10) - 1/(273 + 0)= -Ea
5.763/ [ (3.53x10^-3) - (3.66x10^-3) ] = -Ea
Now just simplify the equation and you should end up with...
5.763/ -1.3x10^-4 = -Ea
-44330.76 = -Ea
44330.76 J/mol = Ea
:) hope that helps.
To determine the activation energy for this reaction, we can use the Arrhenius equation, which relates the rate constant of a reaction to temperature and activation energy.
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
Given that the reaction rate doubles when the temperature increases from 0 degrees Celsius to 10 degrees Celsius, we can use this information to set up an equation. Let's assume the rate constant at 0 degrees Celsius is k1, and k2 is the rate constant at 10 degrees Celsius.
Given:
k2 = 2 * k1
Converting the temperatures to Kelvin:
T1 = 0 + 273.15 = 273.15 K
T2 = 10 + 273.15 = 283.15 K
Now, we can substitute these values into the Arrhenius equation and rearrange the equation to solve for the activation energy (Ea):
2 * k1 = A * exp(-Ea / (R * 283.15 K))
k1 = A * exp(-Ea / (R * 273.15 K))
Dividing these two equations:
2 = exp((Ea / (R * 273.15 K)) - (Ea / (R * 283.15 K)))
2 = exp((Ea / (R * 273.15 K)) * (1 - (273.15 / 283.15)))
Now, take the natural logarithm (ln) of both sides:
ln(2) = ((Ea / (R * 273.15 K)) * (1 - (273.15 / 283.15)))
Rearranging the equation to solve for Ea:
Ea = -R * 273.15 K * ln(2) / (ln(2) - (273.15 / 283.15))
Now we can substitute the values of R and solve for Ea.