Temperature Analysis from Cooling Curve Graph
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What is the initial temperature ($^\circ C$) of the solution?
22.5
What is the final temperature ($^\circ C$) of the solution?
This question includes visual content: A Cartesian coordinate system graph. The y-axis is labeled 'Temperature (degrees Celsius)' ranging from 20 to 45. The x-axis is labeled 'Time (s)' ranging from -120 to 600. Several black data points are plotted. Before time $t=0$, there are points at approximately $-60s$ and $-30s$ with temperature around $22.5^\circ C$. At $t=30s$, the temperature jumps to approximately $43^\circ C$. From $t=30s$ to $t=330s$, data points show a cooling trend, with a red line of best fit drawn through them. After $t=360s$, the temperature plateaus and remains constant at approximately $37.5^\circ C$ or $38^\circ C$ until $t=600s$.
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Step by Step Written Solution
In this problem, we need to analyze a temperature versus time graph from a calorimetry experiment to determine the initial and final temperatures of a solution.
Calorimetry Data Analysis
Let's start with the initial temperature. Look at the data points before the reaction begins, which is the time before zero seconds.
1. Initial Temperature ($T_i$)
We can see data points at negative sixty and negative thirty seconds. These points are located halfway between twenty and twenty-five degrees Celsius on the vertical axis.
The value exactly in the middle of twenty and twenty-five is twenty-two point five degrees Celsius. This represents the stable temperature of the solution before mixing.
Now, let's determine the final temperature. In calorimetry, the final temperature is often determined by extrapolating the cooling curve back to the time of mixing, which is time zero.
2. Final Temperature ($T_f$)
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