Chemistry question! density=mass/volume?

Question

An empty vial weighs 53.99 g.

(a) If the vial weighs 176.55 g when filled with liquid mercury (d = 13.53 g/cm3), what is its volume? the answer is: 9.058 cm3

(b) How much would the vial weigh if it were filled with water (d = 0.997 g/cm3 at 25°C)? ____________ g

Answer 1

a)

Mass of Hg=176.55 g-53.99 g=122.56 g

Density=mass/volume

d=m/v

dv=(m/v)v

dv=m

(dv)/d=m/d

v=m/d

Volume=mass/density=122.56 g/(13.53 g/cm³)=9.058 cm³

b)

Density=mass/volume

d=m/v

dv=(m/v)v

dv=m or m=dv

Mass=density times volume=0.997 g/cm³ x 9.058 cm³=9.03 g

Mass of Vial+water=9.03 g+53.99 g=63.02 g

Do you see your mistake? You found the mass of the water but the question asks for the mass of the vial filled with water, not just the mass of the water.

Answer 2

I guess you have to assume that the mercury from problem (a) is filled to maximum volume.

So I think in this case, you would use mass = density * volume.

(0.997 g/cm^3)(9.058 cm^3) = 9.031 g