[oceanbreeze]

Question: A student collected four different samples of a substance and generated a Mass vs. Volume graph. What is the density of the student's sample?

When the samples are graphed, the graph indicates: y = 0.784x. Is the density the same as the slope? Therefore, would the density be 0.784 g/ML?

Info from four samples:
Volume = 2.19, Mass = 1.80
Volume = 5.57, Mass = 4.13
Volume = 8.34, Mass = 6.70
Volume = 4.08, Mass = 3.15

Thank you!

[Tdha]

Theoretically, at constant temperature and pressure the density must be independent from the mass of the system (so the constant before x must be 1). The "0,784x" is caused by the inaccurate measurement.
I think, he should calculate independent density values, and use them to calculate an average.

[curiouscat]

Theoretically, at constant temperature and pressure the density must be independent from the mass of the system (so the constant before x must be 1). The "0,784x" is caused by the inaccurate measurement.

Wrong. The constant is the density!

[Tdha]

OK, you're right. I misunderstood something.
But how calculates y=0,784x equation? What is "x"?

[oceanbreeze]

I'm not sure what "x" is, other than an unknown variable in the slope equation "y=mx+b". The equation for slope here is y=0.784x, but I don't know how to derive the answer from the equation or data.

[Borek]

mass = 0.784 * volume

[gritch]

Question: A student collected four different samples of a substance and generated a Mass vs. Volume graph. What is the density of the student's sample?

I'm not sure what "x" is, other than an unknown variable in the slope equation "y=mx+b". The equation for slope here is y=0.784x, but I don't know how to derive the answer from the equation or data.

In this we're setting our massto our y-coordinate and our volume to our x-coordinate. So here we can read our y=mx+b in terms of physical properties as:
Mass=m*Volume + b.
Where m is a property that relates the mass of the sample to its volume and b is the initial volume of the sample without mass. Given a sample with no mass also has no volume we can set b=0(basically we have the boundary condition that when x=0 y must also equal 0). The physical property that relates mass to volume to mass is known as density therefore equation simply becomes:
Mass = Density * Volume

[Tdha]

Okay, understand. But my excel calculated 0,794 instead 0,784

[gritch]

Okay, understand. But my excel calculated 0,794 instead 0,784

Note in the equation excel has provided does not have b=0. If you use the LINEST command and fix the intercept to 0 you do indeed get 0.784.

[Tdha]

Thanks, I've learned something today too.