Question

1. a block of aluminum occupies a volume of 15.0 ml and weighs 40.5 g. what is its density? 2) mercury metal is poured into a graduated cylinder that holds exactly 22.5 ml. the mercury used to fill the cylinder weighs 306.0 g. from this information, calculate the density of mercury. 3) what is the weight of the ethyl alcohol that exactly fills a 200.0 ml container? the density of ethyl alcohol is 0.789 g/ml. 4) a rectangular block of copper metal weighs 1896 g. the dimensions of the block are 8.4 cm by 5.5 cm by 4.6 cm. from this data, what is the density of copper?

Explanation:

Step1: Recall density formula

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

Question 1

Step1: Identify mass and volume

Given $m = 40.5\ g$ and $V=15.0\ mL$.

Step2: Calculate density

$
ho=\frac{40.5\ g}{15.0\ mL}=2.7\ g/mL$

Question 2

Step1: Identify mass and volume

Given $m = 306.0\ g$ and $V = 22.5\ mL$.

Step2: Calculate density

$
ho=\frac{306.0\ g}{22.5\ mL}=13.6\ g/mL$

Question 3

Step1: Recall mass - density - volume relation

We know $
ho=\frac{m}{V}$, so $m=
ho V$.

Step2: Identify density and volume

Given $
ho=0.789\ g/mL$ and $V = 200.0\ mL$.

Step3: Calculate mass

$m=0.789\ g/mL\times200.0\ mL = 157.8\ g$

Question 4

Step1: Calculate volume of the block

The volume of a rectangular - block $V=l\times w\times h$, where $l = 8.4\ cm$, $w = 5.5\ cm$ and $h = 4.6\ cm$. So $V=8.4\times5.5\times4.6\ cm^{3}=8.4\times25.3\ cm^{3}=212.52\ cm^{3}$.

Step2: Identify mass

Given $m = 1896\ g$.

Step3: Calculate density

$
ho=\frac{1896\ g}{212.52\ cm^{3}}\approx8.92\ g/cm^{3}$

Answer:

1. $2.7\ g/mL$
2. $13.6\ g/mL$
3. $157.8\ g$
4. $\approx8.92\ g/cm^{3}$