Вычислите, во сколько раз увеличится скорость реакции при повышении температуры от 50 до 90 °С, если температурный коэффициент скорости равен 3.8136189

1. Break Down the Problem

To determine how much the reaction rate increases when temperature is raised from 50 °C to 90 °C with a temperature coefficient given, we will follow these steps:

1. Identify the temperature increase.
2. Apply the temperature coefficient to find the increase in reaction rate.

2. Relevant Concepts

The temperature coefficient of a reaction (often denoted as $Q_{10}$) represents how much the rate of a reaction increases with a 10 °C rise in temperature.

3. Analysis and Detail

1. Calculate the change in temperature: $\Delta T = 90 \, °C - 50 \, °C = 40 \, °C$

2. Determine how many 10 °C intervals fit into 40 °C: $\text{Number of intervals} = \frac{40 \, °C}{10 \, °C} = 4$

3. Calculate the increase in reaction rate: Since the coefficient $Q_{10}$ is 3.8136189, the increase in reaction rate can be calculated as: $\text{Increase in rate} = Q_{10}^{\text{number of intervals}} = (3.8136189)^4$

4. Verify and Summarize

Now we need to calculate $(3.8136189)^4$.

$(3.8136189)^4 \approx 2.5 \times 3.8136189 = 145.36$ After performing the calculation: $(3.8136189)^4 \approx 223.82$

Final Answer

The speed of the reaction will increase approximately 223.82 times when the temperature is raised from 50 °C to 90 °C.