Question

when the students combined 25 grams of reactant 1 with water, they collected the temperature measurements displayed in the table below.
temperature measurements
time in min. | temp in °c
0 | 22
0.5 | 21
1.0 | 18
1.5 | 17
2.0 | 15
2.5 | 13
3.0 | 11
3.5 | 9
4.0 | 8
4.5 | 7
5.0 | 6

Explanation:

Assuming the problem is to find the relationship (like slope, or analyze the data), let's say we want to find the slope of the line relating Time (min) and Temperature (°C) to see the rate of temperature change.

Step1: Identify two points

Let's take the first two points: (0, 22) and (5, 21). The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Apply the slope formula

Substitute $x_1 = 0, y_1 = 22, x_2 = 5, y_2 = 21$ into the formula: $m = \frac{21 - 22}{5 - 0} = \frac{-1}{5} = -0.2$. This means the temperature decreases by 0.2 °C per minute (for these two points). To check with another pair, say (5,21) and (10,18): $m = \frac{18 - 21}{10 - 5} = \frac{-3}{5} = -0.6$ (wait, maybe my initial point choice was off, let's take (0,22) and (10,18): $m = \frac{18 - 22}{10 - 0} = \frac{-4}{10} = -0.4$. Wait, maybe the data is for a reaction cooling? Let's list all points:

Time (min): 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Temp (°C): 22, 21, 18, 17, 15, 13, 11, 9, 8, 7, 6

Let's take (0,22) and (50,6). Slope $m = \frac{6 - 22}{50 - 0} = \frac{-16}{50} = -0.32$.

Alternatively, maybe the problem is to find the average rate of change over the entire time. The total time change is 50 - 0 = 50 minutes. Total temperature change is 6 - 22 = -16 °C. Average rate: $\frac{-16}{50} = -0.32$ °C per minute.

Answer:

The average rate of temperature change from 0 to 50 minutes is -0.32 °C per minute (or specific rate between points as calculated above). If the problem was to find the slope (rate), this is the calculation.