#### Question

The mass of an empty density bottle is 21.8 g, when filled completely with water is 41.8 g and when filled completely with liquid it is 40.6 g. Find :

(a) the volume of density bottle.

(b) the relative density of liquid.

#### Solution

Density of water is 1 g Cm^{3}

∴ Volume of density bottle = weight of water in grams completely filling the bottle

(a) Volume of density bottle:

Mass of empty density bottle = M_{1} =21.8 g

Mass of bottle + water = M_{2} 41.8 g

∴ Mass of water completely fih1ig the density bottle = M_{2} — M_{1}

=41.8 —21.8

20g

But 1 g of water has volume = 1 cc

∴ Volume of bottle (density bottle) = volume of water =20 c.c. =20 ml

(b) The relative density of liquid:

Mass of 20 c.c. of liquid = (mass of density bottle + mass of 20 c.c of liquid- mass of density bottle)

= 40.6—21.8

= 18.8 g

Mass of 20 C.C of water = 20g

Relative density of liquid

R.D. =` (Mass of 20 c.c of liquid)/(Mass of 20 c.c of water)`=`18.8/20`

=`1.88/2`=0.94