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

Answer:

9.2 grams of ethanol should be added.

Explanation:

Let the mass of ethanol be x

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

Volume of the ethanol =$V_1=\frac{x}{0.80 g/cm^3}$

Mass of chloroform = 5.0 g

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

Volume of the ethanol =$V_2=\frac{5.0 g}{1.5 g/cm^3}=\frac{1}{3}$

Mass of the mixture,m  = x + 5.0 g

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

Volume of the mixture=$V=\frac{m}{1.2 g/cm^3}=\frac{x+5.0 g}{1.2 g/cm^3}$

$V=V_1+V_2$

$\frac{x+5.0 g}{1.2 g/cm^3}=V_1+\frac{1}{3}$

$\frac{x+5.0 g}{1.2 g/cm^3}=\frac{x}{0.80 g/cm^3}+\frac{1}{3}$

Solving for x , we get

x = 9.2 g

9.2 grams of ethanol should be added.