Question

1 - 5 density worksheet
since density shows how many particles (mass) are in a certain amount of space (volume), the formula for density is...
density = mass / volume (mass divided by volume)
the unit for density is grams per cubic centimeter (g/cm³)
calculate the densities of the following objects. you will need a calculator.
round all answers to the tenths place (1 place after the decimal)

1. a shoe - box

mass = 114.0 g volume = 538.5 cm³
density = ______ g/cm³

1. a rock

mass = 22.3 g volume = 8.0 cm³
density = ______ g/cm³

1. a full soda bottle

mass = 609.0 g volume = 591.0 ml

1. a dry sponge

mass = 54.2 g volume = 78.1 cm³
density = ______ g/cm³

1. when a dry sponge absorbs water, which changes most (circle one)?

a. the sponge’s mass
b. neither changes, mass and volume stay the same
c. the sponge’s volume

1. the sponge in question #10 absorbs 277 grams of water. recalculate its density.

*show your work

1. a) you drink all of the soda out of the bottle (from question #9). the soda had a mass of 570 grams. recalculate the density of the empty soda bottle.

*show your work
b) why did the density of the bottle of soda change?

Explanation:

Step1: Recall density formula

Density $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Calculate density of shoe - box

Given $m = 114.0$ g and $V=538.5$ $cm^{3}$. Then $
ho=\frac{114.0}{538.5}\approx0.2$ g/$cm^{3}$.

Step3: Calculate density of rock

Given $m = 22.3$ g and $V = 8.0$ $cm^{3}$. Then $
ho=\frac{22.3}{8.0}=2.8$ g/$cm^{3}$.

Step4: Convert volume of soda bottle to $cm^{3}$

Since $1$ mL=$1$ $cm^{3}$, for a soda - bottle with $V = 591.0$ mL, $V = 591.0$ $cm^{3}$. Given $m = 609.0$ g, then $
ho=\frac{609.0}{591.0}\approx1.0$ g/$cm^{3}$.

Step5: Calculate density of dry sponge

Given $m = 54.2$ g and $V = 78.1$ $cm^{3}$. Then $
ho=\frac{54.2}{78.1}\approx0.7$ g/$cm^{3}$.

Step6: Answer question 11

When a dry sponge absorbs water, its mass increases significantly while its volume changes very little. So the answer is A. the sponge's mass.

Step7: Recalculate density of sponge after absorbing water

New mass $m_{new}=54.2 + 277=331.2$ g, volume $V = 78.1$ $cm^{3}$. Then $
ho=\frac{331.2}{78.1}\approx4.2$ g/$cm^{3}$.

Step8: Calculate mass of empty soda bottle

Mass of full - soda bottle is $m_{full}=609.0$ g, mass of soda is $m_{soda}=570$ g. So mass of empty bottle $m_{empty}=609.0 - 570 = 39$ g, volume $V = 591.0$ $cm^{3}$. Then $
ho=\frac{39}{591.0}\approx0.1$ g/$cm^{3}$.

Step9: Answer part b of question 13

The density of the bottle of soda changed because the mass of the substance inside the bottle changed (from full of soda to empty), while the volume of the bottle remained the same.

Answer:

1. $0.2$ g/$cm^{3}$
2. $2.8$ g/$cm^{3}$
3. $1.0$ g/$cm^{3}$
4. $0.7$ g/$cm^{3}$
5. A. the sponge's mass
6. $4.2$ g/$cm^{3}$
7. a) $0.1$ g/$cm^{3}$

b) The mass of the substance inside the bottle changed while the volume remained the same.