Question

1. a piece of green jade has a mass of 26.123 g. if the sample of jade displaces 50.0 ml of water to 57.5 ml in a graduated cylinder, what is the density of the jade?
2. a 5.00 - cm cube of magnesium has a mass of 217.501 g. what is the density of magnesium metal?
3. aluminum foil is often incorrectly termed tin foil. if the density of tin is 7.28 g/cm³, what is the thickness of a piece of tin foil that measures 5.70 cm by 4.25 cm and has a mass of 0.655 g?
4. (optional) a silver sphere has a mass of 5.492 g and a diameter of 10.0 mm. what is the density of silver metal in grams per cubic centimeter? the volume of a sphere equals 4πr³/3, where π is 3.14, and r is the radius.

Explanation:

3.

Step1: Recall density formula

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

Step2: Identify mass and volume values

The mass of the jade $m = 26.123$ g and the volume of the jade $V=50.0$ mL. Since 1 mL = 1 $cm^{3}$, $V = 50.0$ $cm^{3}$.

Step3: Calculate density

$
ho=\frac{26.123\text{ g}}{50.0\text{ cm}^3}=0.52246$ g/$cm^{3}$

Step1: Recall density formula

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

Step2: Calculate volume of the cube

The volume of a cube with side length $a$ is $V=a^{3}$. Given $a = 5.00$ cm, so $V=(5.00\text{ cm})^{3}=125\text{ cm}^3$.

Step3: Identify mass value

The mass of the magnesium $m = 217.501$ g.

Step4: Calculate density

$
ho=\frac{217.501\text{ g}}{125\text{ cm}^3}=1.740008$ g/$cm^{3}$

Step1: Recall density formula to find volume

From $
ho=\frac{m}{V}$, we can get $V=\frac{m}{
ho}$. Given $m = 0.655$ g and $
ho = 7.28$ g/$cm^{3}$, so $V=\frac{0.655\text{ g}}{7.28\text{ g/cm}^3}\approx0.0900$ $cm^{3}$.

Step2: Recall volume formula for a rectangular - shaped object

The volume of a rectangular - shaped object is $V = l\times w\times h$, where $l = 5.70$ cm, $w = 4.25$ cm and $h$ is the thickness.

Step3: Solve for thickness

$h=\frac{V}{l\times w}=\frac{0.0900\text{ cm}^3}{5.70\text{ cm}\times4.25\text{ cm}}\approx0.00370$ cm

Answer:

$0.522$ g/$cm^{3}$ (rounded to three - significant figures)

4.