Q1.78CP - Chemistry: Molecular Nature Of Matter And Change

Question

At room temperature (20°C) and pressure, the density of air is 1.189 g/L. An object will float in air if its density is less than that of air. In a buoyancy experiment with a new plastic, a chemist creates a rigid, thin-walled ball that weighs 0.12 g and has a volume of 560 .

(a) Will the ball float if it is evacuated?

(b) Will it float if filled with carbon dioxide (d = 1.830 g/L)?

(c) Will it float if filled with hydrogen (d = 0.0899 g/L)?

(d) Will it float if filled with oxygen (d = 1.330 g/L)?

(e) Will it float if filled with nitrogen (d = 1.165 g/L)? 

(f) For any case that will float, how much weight must be added to make the ball sink?       

Step-by-Step Solution

Answer

The answer is,

(a) Yes 

(b) No

(c) Yes

(d) No

(e) No

(f) 0.672 g

Step 1: Density

The density of a substance can be calculated using the mass and volume of the substance. The density can be taken as the ratio of mass and volume of the substance.

Step 2: Subpart (a)

Given, 

Density of air is 1.189 g/L.

Mass of the ball is 0.12g.

Volume of the ball is 560 cubic centimeter (0.56L).

Then the density can be calculated as shown below.

 $\begin{array}{c}\mathrm{d}=\frac{\mathrm{m}}{\mathrm{v}}\\ =\frac{0.12\mathrm{g}}{0.56\mathrm{L}}\\ =0.214\mathrm{g}/\mathrm{L}\end{array}$

Then the density of the evacuated ball is less than the air.

Therefore, the ball will float when it is evacuated.

Step 3: Subpart (b)

The Density of carbon dioxide is 1.830 g/L. 

The ball will not float because the density of carbon dioxide filled in the ball makes it to sink.

Step 4: Subpart (c)

The Density of hydrogen is 0.0899 g/L.

Here the ball will float because the filling of hydrogen did not cause to increase the density of the ball. This is because of the lower density of the hydrogen.

Step 5: Subpart (d)

The Density of nitrogen is 1.330 g/L. 

Here the ball will not float because the density of the ball increases when filled with nitrogen gas, due to higher density of nitrogen.

Step 6: Subpart (e)

The Density of oxygen is 1.165 g/L.

Here the ball will not float because the filling of oxygen causes to increase the density of the ball. This is because of the higher density of the oxygen.

Step 7: Subpart (f)

In first and third case, the ball floats over air.

The mass that must be added to sink is calculated as shown below.

Taking, the density of the ball is raised upto 1.2 g/L.

$\begin{array}{c}\mathrm{d}=\frac{\mathrm{m}}{\mathrm{v}}\\ 1.2\mathrm{g}/\mathrm{L}=\frac{\mathrm{m}}{0.56\mathrm{L}}\\ \mathrm{m}=0.672\mathrm{g}\end{array}$