Question

show your work and include units for the following problems.

1. what is the density of a block of metal that has a mass of 250 grams and a volume of 40 cm³?
2. what is the density of 0.196 grams of carbon dioxide gas if this gas has a volume of 120 cm³?
3. a rectangular sample has a length of 2 cm, width of 2 cm, and height of 5 cm.

a) what is the volume of this sample?
b) if the mass of this sample is 94 grams, what is its density?
c) what is the specific gravity of this sample?
d) will this sample float or sink in water?

1. an 89.6 grams sample of copper has a volume of 10 cm³. what is the density of this piece of copper?

Explanation:

Step1: Recall density formula

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

Problem 1

Step1: Identify mass and volume values

$m = 250$ g, $V=40$ cm³

Step2: Calculate density

$
ho=\frac{250\text{ g}}{40\text{ cm}^3}=6.25$ g/cm³

Problem 2

Step1: Identify mass and volume values

$m = 0.196$ g, $V = 120$ cm³

Step2: Calculate density

$
ho=\frac{0.196\text{ g}}{120\text{ cm}^3}\approx0.00163$ g/cm³

Problem 3a

Step1: Recall volume formula for rectangular - solid

$V=l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height.

Step2: Substitute values

$V = 2\text{ cm}\times2\text{ cm}\times5\text{ cm}=20$ cm³

Problem 3b

Step1: Identify mass and volume values

$m = 94$ g, $V = 20$ cm³ (from 3a)

Step2: Calculate density

$
ho=\frac{94\text{ g}}{20\text{ cm}^3}=4.7$ g/cm³

Problem 3c

Step1: Recall specific - gravity formula

Specific gravity $SG=\frac{
ho_{substance}}{
ho_{water}}$, and $
ho_{water}=1$ g/cm³

Step2: Substitute density value (from 3b)

$SG=\frac{4.7\text{ g/cm}^3}{1\text{ g/cm}^3}=4.7$

Problem 3d

Step1: Compare density with water density

Since $
ho_{sample}=4.7$ g/cm³ and $
ho_{water}=1$ g/cm³, and $
ho_{sample}>
ho_{water}$

Step2: Determine result

The sample will sink.

Problem 4

Step1: Identify mass and volume values

$m = 89.6$ g, $V = 10$ cm³

Step2: Calculate density

$
ho=\frac{89.6\text{ g}}{10\text{ cm}^3}=8.96$ g/cm³

Answer:

1. $6.25$ g/cm³
2. $0.00163$ g/cm³

3.
a. $20$ cm³
b. $4.7$ g/cm³
c. $4.7$
d. Sink

1. $8.96$ g/cm³