5. Gather data: A useful way to compare reaction rates is to record the time required for half of the reactants to react, called the half-life of the reaction. With the Temperature set to 175 °C, click Play. Record the half-life time in the first space of the table below.

Question

|Trial | 175 °C | 145 °C | 100 °C | 65 °C |
| | | | | |
| 1 | | | | |
| | | | | |
| 2 | | | | |

\Mean half-life Show all work \ | | |

Repeat the experiment at different temperatures to complete the table. (Note: To get exact times, you can refer to the TABLE tab.)

6. Calculate: Calculate the mean half-life for each temperature. Fill in these values above.

(Hint: To get an exact mean, first convert each time to seconds by multiplying the minutes value by 60 and adding this to the seconds. To find the mean in seconds, add up the two times and divide by two. Convert the answer back to minutes and seconds.)

7. Analyze: What do your results indicate?

Answer 1

It looks like you're working on a laboratory experiment to analyze the effect of temperature on reaction rates by measuring the half-lives of a chemical reaction. Below, I'll guide you through the completion of the table and the subsequent calculations required. However, since I cannot perform the experiment or gather actual data, I'll illustrate how you would typically proceed based on recorded half-lives.

Example Data Collection

Let's assume you performed your experiments and obtained the following half-lives (in minutes and seconds) for the different temperatures:

| Trial | 175 °C | 145 °C | 100 °C | 65 °C | |-------|------------|-----------|---------|---------| | 1 | 2 min 30 sec | 4 min 15 sec | 8 min 10 sec | 15 min 0 sec | | 2 | 2 min 40 sec | 4 min 5 sec | 8 min 20 sec | 14 min 30 sec |

Step 6: Calculate Mean Half-Life for Each Temperature

Convert each time to seconds:

1. 175 °C:

   • Trial 1: \(2 \times 60 + 30 = 150\) seconds
   • Trial 2: \(2 \times 60 + 40 = 160\) seconds
   • Mean: \((150 + 160) / 2 = 155\) seconds
   • Convert back: \(155 \div 60 = 2\) minutes and \(155 \mod 60 = 35\) seconds → 2 min 35 sec

2. 145 °C:

   • Trial 1: \(4 \times 60 + 15 = 255\) seconds
   • Trial 2: \(4 \times 60 + 5 = 245\) seconds
   • Mean: \((255 + 245) / 2 = 250\) seconds
   • Convert back: \(250 \div 60 = 4\) minutes and \(250 \mod 60 = 10\) seconds → 4 min 10 sec

3. 100 °C:

   • Trial 1: \(8 \times 60 + 10 = 490\) seconds
   • Trial 2: \(8 \times 60 + 20 = 500\) seconds
   • Mean: \((490 + 500) / 2 = 495\) seconds
   • Convert back: \(495 \div 60 = 8\) minutes and \(495 \mod 60 = 15\) seconds → 8 min 15 sec

4. 65 °C:

   • Trial 1: \(15 \times 60 + 0 = 900\) seconds
   • Trial 2: \(14 \times 60 + 30 = 870\) seconds
   • Mean: \((900 + 870) / 2 = 885\) seconds
   • Convert back: \(885 \div 60 = 14\) minutes and \(885 \mod 60 = 45\) seconds → 14 min 45 sec

Completed Table

Now we can fill in the completed table with the calculated means:

| Trial | 175 °C | 145 °C | 100 °C | 65 °C | |-------|-----------|----------|---------------|---------------| | 1 | 2 min 30 sec | 4 min 15 sec | 8 min 10 sec | 15 min 0 sec | | 2 | 2 min 40 sec | 4 min 5 sec | 8 min 20 sec | 14 min 30 sec | | Mean | 2 min 35 sec | 4 min 10 sec | 8 min 15 sec | 14 min 45 sec |

Step 7: Analyze Your Results

The results you've collected indicate a trend related to temperature and reaction rate:

• As the temperature decreases, the mean half-life of the reaction increases. This suggests that higher temperatures facilitate faster reactions, leading to shorter half-lives. This is consistent with the Arrhenius equation and the general principle that increasing temperature increases kinetic energy, thus increasing the rate of chemical reactions.

• Conversely, at lower temperatures, molecules have less kinetic energy, resulting in slower reactions and longer half-lives.

In summary, your data suggests that temperature has a significant effect on chemical reaction rates, affirming the importance of temperature in influencing reaction kinetics.