Question

There are three containers filled with different gases as shown.

Container Gas Density Container Dimensions
A Hydrogen - 0.09 mg/cm3 a cube with sides of 15 cm
B Helium - 0.175 mg/cm3 a rectangular prism with sides of 14 cm, 12 cm, 10 cm
C Nitrogen - 1.251 mg/cm3 a sphere with a diameter of 8 cm
What is the correct order of mass from least to greatest?

Answer 1

$\qquad\qquad\huge\underline{{\sf Answer}}$

As we know,

$\sf \qquad density = \dfrac{mass}{volume}$

So, we can infer that :

$\sf \qquad mass= {density} \cdot{volume}$

Now, let's calculate the mass of gases in each case :

Case A : Hydrogen ~

$\qquad \sf  \dashrightarrow \:mass = 0.09 \times (15) {}^{3}$

$\qquad \sf  \dashrightarrow \:mass = 0.09 \times 3375 {}^{}$

$\qquad \sf  \dashrightarrow \:mass = 303.75 \: \: mg {}^{}$

or

$\qquad \sf  \dashrightarrow \:mass =0. 30375 \: \: g {}^{}$

Case B : Helium ~

$\qquad \sf  \dashrightarrow \:mass =0. 175 \: \cdot \: (14 \sdot 12 \sdot10)$

$\qquad \sf  \dashrightarrow \:mass =0. 175 \: \cdot \: 1680$

$\qquad \sf  \dashrightarrow \:mass =0. 175 \: \cdot \: 294 \: \: mg$

or

$\qquad \sf  \dashrightarrow \:mass = 0.294 \: \: g$

Case C : Nitrogen ~

$\qquad \sf  \dashrightarrow \:mass = 1.251\: \cdot \: \dfrac{4}{3} \cdot3.14 \cdot(4) {}^{3}$

$\qquad \sf  \dashrightarrow \:mass = 0.417\: \cdot \: 803.84$

$\qquad \sf  \dashrightarrow \:mass = 335.201 \: \: mg$

or

$\qquad \sf  \dashrightarrow \:mass = 0.335 \: \: g$

So, the arrangement of masses from least to greatest is :

• (1.) Hydrogen < (2.) Helium < (3.) Nitrogen