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Sagot :
To display the data given in the table in a graphical form, specifically a solubility curve of sugar in water, follow these steps:
1. Organize the Data:
- First, let's list the data clearly from the table:
- At [tex]\(0^\circ C\)[/tex], 89 grams of sugar are dissolved.
- At [tex]\(30^\circ C\)[/tex], 110 grams of sugar are dissolved.
- At [tex]\(60^\circ C\)[/tex], 14.4 grams of sugar are dissolved.
- At [tex]\(90^\circ C\)[/tex], 208 grams of sugar are dissolved.
2. Create a Cartesian Plane:
- On a graph, the x-axis (horizontal line) will represent the temperature in degrees Celsius [tex]\((^\circ C)\)[/tex].
- The y-axis (vertical line) will represent the amount of sugar dissolved in grams.
3. Mark the Axes:
- Label the x-axis with the temperature values: 0, 30, 60, and 90.
- Label the y-axis with the sugar dissolved values. Choose an appropriate scale to include the range of data: from 0 to a bit higher than 208 grams to comfortably fit all points.
4. Plot the Data Points:
- Plot the point corresponding to [tex]\(0^\circ C\)[/tex] at 89 grams:
- (0, 89)
- Plot the point corresponding to [tex]\(30^\circ C\)[/tex] at 110 grams:
- (30, 110)
- Plot the point corresponding to [tex]\(60^\circ C\)[/tex] at 14.4 grams:
- (60, 14.4)
- Plot the point corresponding to [tex]\(90^\circ C\)[/tex] at 208 grams:
- (90, 208)
5. Draw the Solubility Curve:
- Connect the points smoothly to form the solubility curve. Note the trend of the line as you connect the points.
6. Analyzing the Curve:
- The curve will show an initial increase in the amount of sugar dissolved as the temperature rises from [tex]\(0^\circ C\)[/tex] to [tex]\(30^\circ C\)[/tex].
- At [tex]\(60^\circ C\)[/tex], there is a significant drop in the solubility of sugar.
- From [tex]\(60^\circ C\)[/tex] to [tex]\(90^\circ C\)[/tex], the solubility again increases sharply.
Here's how the plotted curve might look on a graph:
[tex]\[ \begin{array}{|c|c|} \hline \text{Temperature} \, (^\circ C) & \text{Sugar Dissolved} \, (\text{grams}) \\ \hline 0 & 89 \\ \hline 30 & 110 \\ \hline 60 & 14.4 \\ \hline 90 & 208 \\ \hline \end{array} \][/tex]
[tex]\[ \text{Graph:} \][/tex]
y-axis
210 | ................................................+
200 |
180 | |
160 | |
140 | |
120 | |
110 | |
90 | |
70 | |
50 | |
30 | |
14.4| |
0 | ................................................+
0 10 20 30 40 50 60 70 90
x-axis
Hence, this graphical representation of the data shows the solubility curve, which will help visualize the change in sugar solubility with increasing temperature.
1. Organize the Data:
- First, let's list the data clearly from the table:
- At [tex]\(0^\circ C\)[/tex], 89 grams of sugar are dissolved.
- At [tex]\(30^\circ C\)[/tex], 110 grams of sugar are dissolved.
- At [tex]\(60^\circ C\)[/tex], 14.4 grams of sugar are dissolved.
- At [tex]\(90^\circ C\)[/tex], 208 grams of sugar are dissolved.
2. Create a Cartesian Plane:
- On a graph, the x-axis (horizontal line) will represent the temperature in degrees Celsius [tex]\((^\circ C)\)[/tex].
- The y-axis (vertical line) will represent the amount of sugar dissolved in grams.
3. Mark the Axes:
- Label the x-axis with the temperature values: 0, 30, 60, and 90.
- Label the y-axis with the sugar dissolved values. Choose an appropriate scale to include the range of data: from 0 to a bit higher than 208 grams to comfortably fit all points.
4. Plot the Data Points:
- Plot the point corresponding to [tex]\(0^\circ C\)[/tex] at 89 grams:
- (0, 89)
- Plot the point corresponding to [tex]\(30^\circ C\)[/tex] at 110 grams:
- (30, 110)
- Plot the point corresponding to [tex]\(60^\circ C\)[/tex] at 14.4 grams:
- (60, 14.4)
- Plot the point corresponding to [tex]\(90^\circ C\)[/tex] at 208 grams:
- (90, 208)
5. Draw the Solubility Curve:
- Connect the points smoothly to form the solubility curve. Note the trend of the line as you connect the points.
6. Analyzing the Curve:
- The curve will show an initial increase in the amount of sugar dissolved as the temperature rises from [tex]\(0^\circ C\)[/tex] to [tex]\(30^\circ C\)[/tex].
- At [tex]\(60^\circ C\)[/tex], there is a significant drop in the solubility of sugar.
- From [tex]\(60^\circ C\)[/tex] to [tex]\(90^\circ C\)[/tex], the solubility again increases sharply.
Here's how the plotted curve might look on a graph:
[tex]\[ \begin{array}{|c|c|} \hline \text{Temperature} \, (^\circ C) & \text{Sugar Dissolved} \, (\text{grams}) \\ \hline 0 & 89 \\ \hline 30 & 110 \\ \hline 60 & 14.4 \\ \hline 90 & 208 \\ \hline \end{array} \][/tex]
[tex]\[ \text{Graph:} \][/tex]
y-axis
210 | ................................................+
200 |
180 | |
160 | |
140 | |
120 | |
110 | |
90 | |
70 | |
50 | |
30 | |
14.4| |
0 | ................................................+
0 10 20 30 40 50 60 70 90
x-axis
Hence, this graphical representation of the data shows the solubility curve, which will help visualize the change in sugar solubility with increasing temperature.
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