Question

1. a 10.0 cm³ sample of copper has a mass of 89.6 g. what is the density of copper?
2. silver has a density of 10.5g/cm³ and gold has a density of 19.3 g/cm³. which would have a greater mass, 5 cm³ of silver or 5 cm³ of gold?
3. five ml of ethanol has a mass of 3.9 g, and 5.0 ml of benzene has a mass of 4.4 g. which liquid is denser?
4. a sample of iron has the dimensions of 2 cm x 3 cm x 2 cm. if the mass of this rectangular - shaped object is 94 g, what is the density of iron?

Explanation:

Question 4

Step1: Recall density formula

Density ($
ho$) is defined as mass ($m$) divided by volume ($V$), so $
ho = \frac{m}{V}$.

Step2: Substitute values

Given $m = 89.6\ \text{g}$ and $V = 10.0\ \text{cm}^3$, substitute into the formula: $
ho=\frac{89.6\ \text{g}}{10.0\ \text{cm}^3}$.

Step3: Calculate density

$\frac{89.6}{10.0}=8.96\ \text{g/cm}^3$.

Step1: Recall mass formula from density

The formula for mass is $m=
ho\times V$, where $
ho$ is density and $V$ is volume.

Step2: Calculate mass of silver

For silver, $
ho = 10.5\ \text{g/cm}^3$ and $V = 5\ \text{cm}^3$. So $m_{\text{silver}}=10.5\ \text{g/cm}^3\times5\ \text{cm}^3 = 52.5\ \text{g}$.

Step3: Calculate mass of gold

For gold, $
ho = 19.3\ \text{g/cm}^3$ and $V = 5\ \text{cm}^3$. So $m_{\text{gold}}=19.3\ \text{g/cm}^3\times5\ \text{cm}^3=96.5\ \text{g}$.

Step4: Compare masses

Since $96.5\ \text{g}>52.5\ \text{g}$, gold has a greater mass.

Step1: Recall density formula

Density $
ho=\frac{m}{V}$.

Step2: Calculate density of ethanol

For ethanol, $m = 3.9\ \text{g}$ and $V = 5\ \text{mL}$ (since $1\ \text{mL}=1\ \text{cm}^3$ for liquid volume). So $
ho_{\text{ethanol}}=\frac{3.9\ \text{g}}{5\ \text{mL}} = 0.78\ \text{g/mL}$.

Step3: Calculate density of benzene

For benzene, $m = 4.4\ \text{g}$ and $V = 5.0\ \text{mL}$. So $
ho_{\text{benzene}}=\frac{4.4\ \text{g}}{5.0\ \text{mL}} = 0.88\ \text{g/mL}$.

Step4: Compare densities

Since $0.88\ \text{g/mL}>0.78\ \text{g/mL}$, benzene is denser.

Answer:

The density of copper is $8.96\ \text{g/cm}^3$.

Question 5