Question

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

Answer 1

`4.49` `"g/cm"^3`

Explanation:

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

The density `rho` of a substance is related by the equation

`rho = "mass"/"volume"`

Density is the mass of a substance per unit volume of that substance, most commonly expressed in units of `"g/cm"^3` (solids), `"g/mL"` (liquids), or `"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` `"mL" = 1` `"cm"^3`. We'll now convert this to units of `"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.

Answer 2

The density of Ti is `"4.49 g/cm"^3`.

Explanation:

To get the density of titanium (Ti) in `"g/cm"^3`, you must first convert the mass in kg to mass in g, and convert volume in liters to `"cm"^3`.

Kilograms`rarr`grams

`"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`rarr`cubic centimeters

`"1 mL=1 cm"^3`

`"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

`"density"="mass"/"volume"`

`"D"_"Ti"=(1550"g")/(345"cm"^3)="4.49 g/cm"^3`