Question

A chemical reaction proceeds of a rate of 50 umol product per second. The temperature is increased and the new rate is 200 umol per second.

What is a good estimation of how many degrees Celsius the temperature was increased?

Group of answer choices

150 °C

10 °C

20 °C

2 °C

None; increasing temperature has no impact on the speed of a reaction.

Answer 1

Step-by-step explanation:

To estimate how many degrees Celsius the temperature was increased, we can use the concept of the temperature dependence of reaction rates, which is described by the Arrhenius equation:

k = A * exp(-Ea / (RT))

where:

k = rate constant of the reaction

A = pre-exponential factor (a constant)

Ea = activation energy of the reaction

R = gas constant (8.314 J/(mol*K))

T = absolute temperature in Kelvin

Since we are interested in the change in temperature, we can use the ratio of the two given rates:

(rate2) / (rate1) = (exp(-Ea / (R * T2))) / (exp(-Ea / (R * T1)))

Since the activation energy (Ea) and the pre-exponential factor (A) are the same for both rates, they will cancel out when we take the ratio. Solving for the change in temperature (ΔT = T2 - T1):

(exp(-Ea / (R * T2))) / (exp(-Ea / (R * T1))) = (rate2) / (rate1)

Taking the natural logarithm of both sides:

ln((rate2) / (rate1)) = -Ea / (R * T2) + Ea / (R * T1)

Now, let's plug in the given values:

rate1 = 50 umol/s

rate2 = 200 umol/s

ln(200/50) = -Ea / (R * T2) + Ea / (R * T1)

ln(4) = Ea / (R * T1) - Ea / (R * T2)

Since ln(4) ≈ 1.3863, we can simplify:

1.3863 = Ea / (R * T1) - Ea / (R * T2)

Next, we need to make a good estimation for the ratio of initial temperature to final temperature (T1 / T2). Let's assume it's in the range of 0.5 to 0.9 (T1 is half to nearly the same as T2).

Let's take T1 / T2 = 0.7 as an example. Now we can solve for Ea:

1.3863 = Ea / (R * T1) - Ea / (R * 0.7 * T1)

1.3863 = Ea * (1 - 1/0.7)

1.3863 = Ea * 0.4286

Ea ≈ 1.3863 / 0.4286 ≈ 3.2334

Now, we can use the activation energy (Ea) to find the change in temperature (ΔT):

ΔT = T2 - T1 ≈ Ea * R ≈ 3.2334 * (8.314 J/(mol*K)) ≈ 26.91 K

Converting to Celsius:

ΔT ≈ 26.91°C

Since we assumed T1 / T2 = 0.7 for the estimation, the actual increase in temperature is approximately 26.91°C. Therefore, a good estimation of how many degrees Celsius the temperature was increased is 26.91°C.

Out of the given answer choices, the closest one to our estimation is:

C. 20 °C

Answer 2

The temperature was increased by 20 °C to achieve a rate of 200 umol per second, following the general rule that reaction rates double for every 10 °C rise in temperature.

The question asks for a good estimation of how many degrees Celsius the temperature was increased if the rate of a chemical reaction went from 50 umol product per second to 200 umol per second. Given the general rule that for many chemical reactions, the rate doubles for every 10 °C increase in temperature, we can deduce the temperature change required to cause the increase in reaction rate observed.

Starting from a rate of 50 umol/s, if the rate doubles for every 10 °C increase:

• At +10 °C, the rate would be 100 umol/s.
• At +20 °C, the rate would be 200 umol/s.

Therefore, the temperature must have been increased by 20 °C to achieve the new rate of 200 umol per second.