Question

part 2 - applied density problems

1. ethanol has a density of 0.789 g/cm³.

a. what is the mass of 225 cm³ of ethanol?
b. what is the volume of 75.0 g of ethanol?

1. what is the density of water in g/ml? what does that mean?
2. the cup is a volume widely used by cooks in the u.s. one cup is equivalent to 237 cm³. one cup of olive oil has a mass of 216 g. what is the density of olive oil? what would you expect to happen if the cup of olive oil is poured into a container of ethanol? why?
3. gold has a density of 19.3 g/cm³. a cube of gold measures 4.23 cm on each edge. what is the volume of the cube? calculate its mass? how many significant figures should you include in your answer and why?

Explanation:

Step1: Recall density formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. We can re - arrange it as $m =
ho V$ and $V=\frac{m}{
ho}$.

Step2: Solve 1a

Given $
ho_{ethanol}=0.789\ g/cm^{3}$ and $V = 225\ cm^{3}$. Using $m=
ho V$, we have $m=(0.789\ g/cm^{3})\times225\ cm^{3}=177.525\ g$.

Step3: Solve 1b

Given $
ho_{ethanol}=0.789\ g/cm^{3}$ and $m = 75.0\ g$. Using $V=\frac{m}{
ho}$, we have $V=\frac{75.0\ g}{0.789\ g/cm^{3}}\approx95.1\ cm^{3}$.

Step4: Answer 2

The density of water is approximately $1\ g/mL$. This means that 1 milliliter of water has a mass of 1 gram.

Step5: Solve 3

Given $m = 216\ g$ and $V=237\ cm^{3}$. Using $
ho=\frac{m}{V}$, we have $
ho=\frac{216\ g}{237\ cm^{3}}\approx0.903\ g/cm^{3}$. Since the density of ethanol is $0.789\ g/cm^{3}$ and the density of olive - oil is $0.903\ g/cm^{3}$, the olive oil will sink in ethanol because the density of olive oil is greater than the density of ethanol.

Step6: Solve 4

The volume of a cube is $V = s^{3}$, where $s = 4.23\ cm$. So $V=(4.23\ cm)^{3}=75.6\ cm^{3}$ (3 significant figures). Using $m=
ho V$ with $
ho = 19.3\ g/cm^{3}$ and $V = 75.6\ cm^{3}$, we have $m=(19.3\ g/cm^{3})\times75.6\ cm^{3}=1460\ g$ (3 significant figures because the side - length of the cube has 3 significant figures and in multiplication, the result has the same number of significant figures as the number with the least significant figures in the values used in the calculation).

Answer:

1a. $177.525\ g$
1b. $95.1\ cm^{3}$

1. Density of water is approximately $1\ g/mL$, meaning 1 mL of water has a mass of 1 g.
2. Density of olive oil is approximately $0.903\ g/cm^{3}$, olive oil will sink in ethanol because its density is greater than that of ethanol.
3. Volume of the cube is $75.6\ cm^{3}$, mass of the cube is $1460\ g$ (3 significant figures).