A reaction is run at 20 degrees celsius and takes 30 minutes to go to completion. How long would it take to complete the same reaction at a temperature of 40 degrees celsius?

*I believe finding the time has something to do with log? I'm not sure

7.5 min. each 10Kelvins doubles reaction rate, as a rule of thumb for first order reacxtions , you can work it more precisely here: https://socratic.org/questions/a-first-order-reaction-is-50-completed-after-30-minutes-this-implies-that-the-ti

for the rule of thumb, and you have to be careful...https://www.chemguide.co.uk/physical/basicrates/temperature.html

Thank you very much! This helped a lot

To calculate the time required for the same reaction at a different temperature, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant of a reaction (k) to the temperature (T) in Kelvin.

The Arrhenius equation is expressed as:

k = Ae^(-Ea/RT)

Where:
k = rate constant
A = frequency factor
Ea = activation energy of the reaction
R = gas constant (8.314 J/mol*K)
T = temperature in Kelvin

To find the time required for the reaction at a different temperature, we need to compare the rate constants at the initial and new temperatures. The ratio of rate constants can be calculated using the equation:

k2/k1 = e^((Ea/R) * (1/T1 - 1/T2))

Where:
k1 = rate constant at the initial temperature (20 degrees Celsius)
k2 = rate constant at the new temperature (40 degrees Celsius)
T1 = initial temperature in Kelvin
T2 = new temperature in Kelvin

First, we need to convert the temperatures to Kelvin. We can do this by adding 273 to the Celsius temperature.

Initial temperature (T1) = 20 + 273 = 293 K
New temperature (T2) = 40 + 273 = 313 K

Now we can plug the values into the equation:

k2/k1 = e^((Ea/R) * (1/T1 - 1/T2))

Now, let's assume the activation energy (Ea) remains constant. In that case, we can simplify the equation to:

k2/k1 = e^(Ea/R) * (1/T1 - 1/T2)

Since we want to find the time required for the reaction to complete, we can consider the ratio of rate constants as the ratio of the reaction times:

t2/t1 = k1/k2

Let's calculate the time ratio:

t2/t1 = k1/k2 = e^(Ea/R) * (1/T1 - 1/T2)

Given that t1 = 30 minutes, let's plug in the values and calculate the time required at the new temperature:

t2/30 = e^(Ea/R) * (1/293 - 1/313)

To determine the value of Ea, we need more information about the reaction. The activation energy is unique for each reaction, so without it, we cannot provide an exact calculation for the time required at the new temperature.

To answer this question, we can use the Arrhenius equation, which relates the rate constant of a reaction to the temperature. The Arrhenius equation is represented as:

k = A * exp(-Ea / (R * T))

Where:
- k is the rate constant of the reaction,
- A is the pre-exponential factor,
- Ea is the activation energy,
- R is the ideal gas constant (8.314 J/(mol*K)), and
- T is the temperature in Kelvin.

To find the time it would take to complete the reaction at a temperature of 40 degrees Celsius (313.15 K), we need to compare the rate constants at both temperatures. Rearranging the Arrhenius equation, we get:

k1 / k2 = (A * exp(-Ea / (R * T1))) / (A * exp(-Ea / (R * T2)))

Simplifying it further, we get:

k1 / k2 = exp(Ea / R) * exp(((1 / T1) - (1 / T2)) * R)

Taking the natural logarithm of both sides, we get:

ln(k1 / k2) = (Ea / R) + ((1 / T1) - (1 / T2)) * R

Now, to find the time it would take for the reaction to complete at 40 degrees Celsius, we need to solve for the ratio of the rate constants (k1 / k2):

ln(k1 / k2) = (Ea / R) + ((1 / T1) - (1 / T2)) * R

Since we have the rate constant at 20 degrees Celsius, we can rearrange the equation to solve for ln(k1 / k2):

ln(k1 / k2) = ((1 / T1) - (1 / T2)) * R

Then, we can use the provided information to calculate the value of ln(k1 / k2). Finally, we can substitute this value into the rearranged equation for ln(k1 / k2) to find the time it would take for the reaction to complete at 40 degrees Celsius.