Q.2.76 - An Introduction to General, Organic, and Biological Chemistry

Question

Suppose you have two 100-mL graduated cylinders. In each cylinder, there is 40.0 mL of water. You also have two cubes: one is lead, and the other is aluminum.

Each cube measures 2.0 cm on each side. After you carefully lower each cube into the water of its own cylinder, what will the new water level be in each of the cylinders?

 Use table 2.8 for density values.

Step-by-Step Solution

Answer

The final volume is 48 mL.

Step 1: Given information

Volume of water = 40.0 mL

Density of lead cube = 11.3 g/ml 

Density of aluminum cube = 2.70 g/ml 

Edge length of cube = 2.0 cm 

New water level in each cylinder = ? 

Step 2: Simplification

The volume of the cube is given by the formula as:

$\mathrm{Volume} \mathrm{of} \mathrm{cube}= {\mathrm{a}}^3$

It is given that edge length = 2.0 cm. Thus, the volume will be:

$$\begin{gathered} \mathrm{Volume} \mathrm{of} \mathrm{cube}= {\mathrm{a}}^3 \\ ={\left(2\right)}^3 \\ =8 {\mathrm{cm}}^3 \end{gathered}$$

As it is known, $1 {\mathrm{cm}}^3=1 \mathrm{mL}$

Thus, $8 {\mathrm{cm}}^3 = 8 \mathrm{mL}$

The calculation for final volume:

The volume of water is given which is 40.00 mL and the calculated volume is 8 mL.

Thus, the total volume will be:

$\mathrm{Total} \mathrm{volume}= 40.00 \mathrm{mL}+8\mathrm{mL}=48 \mathrm{mL}$

Hence, the final volume is 48 mL.