The specific gravity of iron is #7.87# and the density of water at #4.00^@"C"# is #"1.00 g/cm"^3#. You can use this information to find the density of iron. Find the volume occupied by #"9.50 g"# of iron?

1 Answer
Jan 22, 2018

Answer:

Here's what I got.

Explanation:

The idea here is that the specific gravity of a substance is calculated by dividing the density of that substance by the density of a reference substance, which is usually water at #4^@"C"#.

#"SG" = rho_"substance"/rho_ ("H"_2"O at 4"^@"C")#

This means that in order to find the density of a substance, you must multiply its specific gravity by the density of the reference substance.

#rho_"Fe" = "SG" * rho_ ("H"_ 2"O at 4"^@"C")#

Since you are told that water at #4^@"C"# has a density of #"1.00 g cm"^(-3)# and that iron has a specific gravity of #7.87#, you can say that its density must be equal to

#rho_ "Fe" = 7.87 * "1/00 g cm"^(-3)#

#rho_ "Fe" = "7.87 g cm"^(-3)#

Now, the density of a substance tells you the mass of exactly #1# unit of volume of that substance. In this case, the density of iron tells you that #:1 cm"^3# of iron has a mass of #"7.87 g"#.

This means that a #"9.50-g"# sample of iron will occupy a volume of

#9.50 color(red)(cancel(color(black)("g"))) * "1 cm"^3/(7.87color(red)(cancel(color(black)("g")))) = "1.21 cm"^3#

The answer is rounded to three sig figs.