Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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From the graph of Density vs. Concentration (attached), created in Graph 1, what was the relationship between the concentration of the sugar solution and the density of the sugar solution?

### Relationship between Concentration and Density

#### Data Table

| X-value | Y-values |
|---------|----------|
| 3.2     | 1.007    |
| 5.76    | 1.013    |
| 3.84    | 1.0      |
| 7.68    | 1.019    |

#### Analysis

The data presented in the table displays the relationship between the concentration (%m/v) and the corresponding density (g/ml). The `X-value` column represents the concentration of a solution, while the `Y-values` column represents the density of the solution measured at those concentrations.

#### Graph Explanation

The graph titled "Relationship between Concentration and Density" is a scatter plot with a linear regression line summarizing the data from the table. 

- **X-axis:** The concentration (%m/v) ranging from 0 to 10.
- **Y-axis:** The density (g/ml) ranging from 0.995 to 1.02.

Key features of the graph:

- Each blue dot represents a data point from the table.
- The blue dashed line indicates the linear trend of the relationship between concentration and density.
  
The equation of the linear regression line is:

\[ y = 0.0035x + 0.9916 \]

Where:

- *y* represents the density (g/ml).
- *x* represents the concentration (%m/v).
  
The R-squared value (R²) is 0.7755, indicating that approximately 77.55% of the variance in density is explained by the concentration levels.

This visual and mathematical relationship depicts that as the concentration of the solution increases, its density tends to increase linearly.
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Transcribed Image Text:### Relationship between Concentration and Density #### Data Table | X-value | Y-values | |---------|----------| | 3.2 | 1.007 | | 5.76 | 1.013 | | 3.84 | 1.0 | | 7.68 | 1.019 | #### Analysis The data presented in the table displays the relationship between the concentration (%m/v) and the corresponding density (g/ml). The `X-value` column represents the concentration of a solution, while the `Y-values` column represents the density of the solution measured at those concentrations. #### Graph Explanation The graph titled "Relationship between Concentration and Density" is a scatter plot with a linear regression line summarizing the data from the table. - **X-axis:** The concentration (%m/v) ranging from 0 to 10. - **Y-axis:** The density (g/ml) ranging from 0.995 to 1.02. Key features of the graph: - Each blue dot represents a data point from the table. - The blue dashed line indicates the linear trend of the relationship between concentration and density. The equation of the linear regression line is: \[ y = 0.0035x + 0.9916 \] Where: - *y* represents the density (g/ml). - *x* represents the concentration (%m/v). The R-squared value (R²) is 0.7755, indicating that approximately 77.55% of the variance in density is explained by the concentration levels. This visual and mathematical relationship depicts that as the concentration of the solution increases, its density tends to increase linearly.
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