Question

A spherical vessel (diameter = 5.00 cm) when empty has a mass of 12.00 g. What is the greatest volume of water in mL that can be placed in the vessel and still have the vessel float at the surface of benzene? (Given: density of water = 1.00 g/cm³; density of benzene = 0.879 g/cm³)

Answer 1

Given,

the diameter of the spherical vessel = 5.00 cm

Mass of empty vessel = 12.00 g

Density of water = 1.00 g /cm³

Density of benzene = 0.879 g /cm³

Firstly calculating the radium os the spherical vessel,

Radius = Diameter / 2 = 5.00 cm / 2 = 2.5 cm

Now,

The Volume of spherical vessel(V) = (4/3)r³

Substituting the values and solving for V,

V = (4/3) x 3.14 x (2.5 cm)³

V = 65.42 cm³

now, the density of the spherical vessel is,

D = Mass / Volume

D = 12.00 g / 65.42 cm³

D = 0.1834 g /cm³

Since, the density of spherical vessel is less than the density of benzene, thus the vessel float at the surface of benzene.

Now,

We have to calculate the greatest volume of water in mL that can be placed in the vessel and still have the vessel float at the surface,

(Mass of vessel + Mass of water) / Volume of vessel = Density of benzene

(Mass of vessel + Mass of water) = Density of benzene x Volume of vessel

(Mass of vessel + Mass of water) = 0.879 g /cm³ x 65.42 cm³

(12.00 g + Mass of water) = 57.5 g

Mass of water = 57.5 g - 12.00 g

Mass of water = 45.5 g

Converting the mass of water to volume by using the density of water,

= 45.5 g x ( 1.00 cm³ / 1.00 g)

= 45.5 cm³ OR 45.5 mL of water