[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
As we know,
[tex] \sf \qquad density = \dfrac{mass}{volume} [/tex]
So, we can infer that :
[tex] \sf \qquad mass= {density} \cdot{volume} [/tex]
Now, let's calculate the mass of gases in each case :
Case A : Hydrogen ~
[tex]\qquad \sf \dashrightarrow \:mass = 0.09 \times (15) {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \:mass = 0.09 \times 3375 {}^{} [/tex]
[tex]\qquad \sf \dashrightarrow \:mass = 303.75 \: \: mg {}^{} [/tex]
or
[tex]\qquad \sf \dashrightarrow \:mass =0. 30375 \: \: g {}^{} [/tex]
Case B : Helium ~
[tex]\qquad \sf \dashrightarrow \:mass =0. 175 \: \cdot \: (14 \sdot 12 \sdot10)[/tex]
[tex]\qquad \sf \dashrightarrow \:mass =0. 175 \: \cdot \: 1680[/tex]
[tex]\qquad \sf \dashrightarrow \:mass =0. 175 \: \cdot \: 294 \: \: mg[/tex]
or
[tex]\qquad \sf \dashrightarrow \:mass = 0.294 \: \: g[/tex]
Case C : Nitrogen ~
[tex]\qquad \sf \dashrightarrow \:mass = 1.251\: \cdot \: \dfrac{4}{3} \cdot3.14 \cdot(4) {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \:mass = 0.417\: \cdot \: 803.84[/tex]
[tex]\qquad \sf \dashrightarrow \:mass = 335.201 \: \: mg[/tex]
or
[tex]\qquad \sf \dashrightarrow \:mass = 0.335 \: \: g[/tex]
So, the arrangement of masses from least to greatest is :
- (1.) Hydrogen < (2.) Helium < (3.) Nitrogen
