Question

How many grams of ethanol (density 0.80 g/cm 3) should be added to 5.0 g of chloroform (density 1.5 g/cm 3) if the resulting mixture is to have a density of 1.2 g/cm 3? Assume that the fluids do not change their volumes when they are mixed.

Answer 1

9.2 grams of ethanol should be added.

Step-by-step explanation:

Let the mass of ethanol be x

Density of an ethanol =
`d_1=0.80 g/cm^3`

Volume of the ethanol =
`V_1=(x)/(0.80 g/cm^3)`

Mass of chloroform = 5.0 g

Density of an chloroform=
`d_2=1.5 g/cm^3`

Volume of the ethanol =
`V_2=(5.0 g)/(1.5 g/cm^3)=(1)/(3)`

Mass of the mixture,m = x + 5.0 g

Density of the mixture =
`d=1.2 g/cm^3`

Volume of the mixture=
`V=(m)/(1.2 g/cm^3)=(x+5.0 g)/(1.2 g/cm^3)`

`V=V_1+V_2`

`(x+5.0 g)/(1.2 g/cm^3)=V_1+(1)/(3)`

`(x+5.0 g)/(1.2 g/cm^3)=(x)/(0.80 g/cm^3)+(1)/(3)`

Solving for x , we get

x = 9.2 g

9.2 grams of ethanol should be added.