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

Answer:

#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.

Jun 18, 2017

Answer:

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#