Question

Heptane and water do not mix, and heptane has a lower density (0.684 g/mL) than water (1.00 g/mL). A 100 mL graduated cylinder with an inside diameter of 3.200 cm contains 39.0 g of heptane and 32.0 g of water. Before we can determine the height of the liquid column, we need to know the total volume of liquid in the cylinder. Which equation expresses the total volume in terms of the volumes of heptane and water?

Answer 1

We know that ,

1mL = 1cm3.......(1)

density = mass/volume .......(2)

or

VOLUME = mass /density .......(3)

Calculation for water

mass of water = 32.0g

density of water = 1g/mL

using equation number (3)

VOLUME of water = (32.0g)/(1.0g/mL)

VOLUME of water = 32.0mL

​​​​​​.

Calculation for Heptane

Mass of Heptane = 39.0g

Density of Heptane = 0.684g/mL

Using the equation number (3)

Volume of Heptane = (39.0g)/(0.684g/ML)

Volume of Heptane = 57.02mL

Total volume = volume of water + volume of Heptane

Total volume = 32.0mL +57.02mL

Total volume = 89.02mL

Using equation number (1)

Total volume = 89.0cm3

Step(3)

Volume of cylinder will be given as follows

V = πr​​​​​2​​​​h .........(4)

Or

V = (1/4)πd​​​​2​​​​h. ..........(5)

Where,

V = total volume = 89.02cm3

π = constant = (22/7)

r = radius of cylinder

d = diameter of cylinder = 3.200cm

h = hight

So,

Putting the all value in equation number (5)

89.02cm3 = (1/4)(22/7)(3.200cm)2h

89.02cm2 = (0.25)(3.14)(10.24cm2)h

89.02cm3 = (8.046cm2)h

h = (89.02cm3)/(8.046cm2)

h = 11.064cm

Height of liquid = 11.064cm