# A "1.55 kg" sample of Titanium has a volume of "0.345 L". What is its density in "g/cm"^3"?

##### 2 Answers
Jun 18, 2017

$4.49$ ${\text{g/cm}}^{3}$

#### Explanation:

We're asked to find the density of the $\text{Ti}$ sample given how much volume it displaces (which is its volume; in $\text{L}$) and its mass (in $\text{kg}$).

The density $\rho$ of a substance is related by the equation

$\rho = \text{mass"/"volume}$

Density is the mass of a substance per unit volume of that substance, most commonly expressed in units of ${\text{g/cm}}^{3}$ (solids), $\text{g/mL}$ (liquids), or $\text{g/L}$ (gases). Since titanium metal is a solid, we'll be expressing our units practically in grams per cubic centimeter.

The density of the titanium sample (without conversions) is

rho = (1.55"kg")/(0.345"L") = color(red)(4.49 color(red)("kg/L"

Remember that $1$ $\text{mL} = 1$ ${\text{cm}}^{3}$. We'll now convert this to units of ${\text{g/cm}}^{3}$, using dimensional analysis:

color(red)(4.49)(cancel("kg"))/(cancel("L"))((10^3"g")/(1cancel("kg")))((1cancel("L"))/(10^3cancel("mL")))((1cancel("mL"))/(1"cm"^3))= color(blue)(4.49 color(blue)("g/cm"^3

Thus, the density of the titanium is color(blue)(4.49 grams per cubic centimeter.

Jun 18, 2017

The density of Ti is ${\text{4.49 g/cm}}^{3}$.

#### Explanation:

To get the density of titanium (Ti) in ${\text{g/cm}}^{3}$, you must first convert the mass in kg to mass in g, and convert volume in liters to ${\text{cm}}^{3}$.

Kilograms$\rightarrow$grams

$\text{1 kg=1000 g}$

1.55color(red)cancel(color(black)("kg Ti"))xx(1000"g")/(1color(red)cancel(color(black)("kg")))="1550 g Ti"

Liters$\rightarrow$cubic centimeters

${\text{1 mL=1 cm}}^{3}$

${\text{1 L=1000 mL=1000 cm}}^{3}$

0.345color(red)cancel(color(black)("L H"_2"O"))xx(1000"cm"^3)/(1color(red)cancel(color(black)("L")))="345 cm"^3" H"_2"O"

Density of Titanium

$\text{density"="mass"/"volume}$

${\text{D"_"Ti"=(1550"g")/(345"cm"^3)="4.49 g/cm}}^{3}$