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Each pair of mass and volume values (for each cylinder) will be plotted on a scatter plot, with mass on the axis and volume on the x-axis. A best-fit line will then be applied to the plotted data. How will you calculate the value of the slope of this best-fit line? How will the value of the slope help you identify the unknown material that the cylinders are made of?

Each pair of mass and volume values (for each cylinder) will be plotted on a scatter plot, with mass on the axis and volume on the x-axis. A best-fit line will then be applied to the plotted data. How will you calculate the value of the slope of this best-fit line? How will the value of the slope help you identify the unknown material that the cylinders are made of?

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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b. Each pair of mass and volume values (for each cylinder) will be plotted on a scatter plot, with mass on the y- axis and volume on the x-axis. A best-fit line will then be applied to the plotted data. How will you calculate the value of the slope of this best-fit line? How will the value of the slope help you identify the unknown material that the cylinders are made of?
Transcribed Image Text:b. Each pair of mass and volume values (for each cylinder) will be plotted on a scatter plot, with mass on the y- axis and volume on the x-axis. A best-fit line will then be applied to the plotted data. How will you calculate the value of the slope of this best-fit line? How will the value of the slope help you identify the unknown material that the cylinders are made of?
The equation of this best-fit line will have the familiar form y = mx + b, where m represents the slope of the line, and b represents the y-intercept. This is illustrated in the figure below. Mass Best-fit line + Ax Volume Ay The y-intercept (b) is the point on the y-axis where the line crosses the axis. In this experiment, the value of b should be equal to zero. This is because if there is no mass, the volume must also be zero. However, note that your best-fit line might not pass exactly through the origin (0,0) due to experimental error - but it should be quite close. The slope of the line (m) is the change in the y-axis values divided by the change in x-axis values (or, rise over run): m= m = Best-fit line equation: y = mx + b b=y-intercept m = slope AyY₁-Y₂ = x₁ - x₂ Ax Since Ay is really the change in mass (Amass), and Ax is really the change in volume (Avolume), this means that the slope of the best-fit line yields the density of the unknown material: Ay Ax Amass Avolume Once the density is determined in this manner, it will be used to identify the unknown material analyzed. = density
Transcribed Image Text:The equation of this best-fit line will have the familiar form y = mx + b, where m represents the slope of the line, and b represents the y-intercept. This is illustrated in the figure below. Mass Best-fit line + Ax Volume Ay The y-intercept (b) is the point on the y-axis where the line crosses the axis. In this experiment, the value of b should be equal to zero. This is because if there is no mass, the volume must also be zero. However, note that your best-fit line might not pass exactly through the origin (0,0) due to experimental error - but it should be quite close. The slope of the line (m) is the change in the y-axis values divided by the change in x-axis values (or, rise over run): m= m = Best-fit line equation: y = mx + b b=y-intercept m = slope AyY₁-Y₂ = x₁ - x₂ Ax Since Ay is really the change in mass (Amass), and Ax is really the change in volume (Avolume), this means that the slope of the best-fit line yields the density of the unknown material: Ay Ax Amass Avolume Once the density is determined in this manner, it will be used to identify the unknown material analyzed. = density
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