Answers for Group Activity: Graphing Density

  1. The graph of volume (x-axis) vs. mass (y-axis) for the given data resembles the graph of a straight line. It resembles the mathematical form of the straight line: y = mx + b.
  2. The kind of proportion shown on the graph is a direct proportion. When volume increases, so does mass and vice versa. When volume decreases, so does mass and vice versa.
  3. The value of the slope of the graph represents the density of the substance. (The slope of the copper line should be close to 8.9 g/mL and the slope of the aluminum graph should be close to 2.7 g/mL—do not express slopes as ratios of the form x/y: calculate what the ratio is as a single decimal number).
  4. The units of the slope of these graphs are g/mL since the y-axis has units of grams and the x-axis has units of milliliters.
  5. Using the graph means following the line showing 15.5 g over to the best-fit line you drew for aluminum and then going down to the x-axis to read off the volume. It should be close to 5.7 mL.
  6. Using the equation of the line to find the volume works as follows:
    y = (2.7 g/mL)x + 0.02 g
    let y = 15.5 g since the y-axis is mass in grams
    15.5 g = (2.7 g/mL)x + 0.02 g
    15.5 g - 0.02 g = (2.7 g/mL)x
    so x = (15.48 g)/(2.7 g/mL) = 5.7 mL
  7. The slope of the line for copper is steeper than the slope of the line for aluminum because copper is a more dense metal than aluminum is. The slope of these lines is the numerical value of the density of each metal so since they have different densities, they have different slopes.
  8. The y-intercepts from your graphs should be close to zero and you should calculate them algebraically rather than reading them off of the graph. (Use the slope you find and one of the points on the line you drew to find the y-intercept). Reasonable values would be anywhere from 0.01 to 0.5. The units of the y-intercept have to be grams (g) because the y-axis has units of grams and x = 0 at the y-intercept.
  9. In an ideal world with ideal (that is, error free) data the y-intercept should be exactly zero for both graphs. This is because when there is no mass for a metal it also has zero volume (or no volume means no mass). The y-intercept is not zero probably because of systematic error in the mass measurements so that they average out to be a little too high relative to the true mass. If the y-intercept is negative then the systematic error may be that the measurements averaged out as too low.
    Your graphs must have the following features:
  10. Labels with units and numbers for both axes
  11. Labeled data points or lines for aluminum and copper
  12. A line of best fit
  13. Equations for both lines