Question

The drain cleaner, drainex contains small bits of aluminium which reacts with caustic soda to produce hydrogen. What volume of dihydrogen at ${\text{20}}{\,^{\text{o}}}{\text{C}}$ and one bar will be released when $0.15$ g of aluminium reacts?

Answer 1

To answer this question we should know the ideal gas law and mole formula. We will determine the moles of aluminium. Then we will write the balance equation. By using equation we can compare the moles of aluminium with moles of dihydrogen we can determine the moles of dihydrogen. Then by using the ideal gas equation we can determine the volume of dihydrogen.

Formula used: ${\text{mole = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
${\text{pV = nRT}}$

Complete step-by-step answer:
Now, we will determine the mole of each gas as follows:
${\text{mole = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
The molar mass of aluminium is $26.98$gm/mol.
On substituting $0.15$ g for mass and $26.98$gm/mol for molar mass.
${\text{mole = }}\,\dfrac{{0.15}}{{26.98}}$
${\text{mole = }}\,5.56 \times {10^{ - 3}}$
So, the moles of aluminium is $5.56 \times {10^{ - 3}}$.
The equation of reaction of aluminium with caustic soda is as follows:
${\text{2Al}}\,\,{\text{ + }}\,{\text{2}}\,{\text{NaOH}}\,{\text{ + }}\,{\text{2}}\,{{\text{H}}_{\text{2}}}{\text{O}}\, \to \,2\,{\text{NaAl}}{{\text{O}}_2}\, + \,{\text{3}}{{\text{H}}_{\text{2}}}$
From the above equation we can say that two moles of aluminium is producing three moles of dihydrogen. So, $5.56 \times {10^{ - 3}}$ moles of aluminium will produce,
$2\,\,{\text{mol}}\,\,{\text{Al}}\,\,{\text{ = }}\,\,{\text{3}}\,\,{\text{mol}}\,\,\,{{\text{H}}_{\text{2}}}$
$5.56 \times {10^{ - 3}}\,\,{\text{mol}}\,\,{\text{Al}}\,\,{\text{ = }}\,\,8.34 \times {10^{ - 3}}\,{\text{mol}}\,\,{{\text{H}}_{\text{2}}}$
So, $5.56 \times {10^{ - 3}}$ moles of aluminium will give $8.34 \times {10^{ - 3}}$ moles of dihydrogen.
The formula of the ideal gas is as follows:
${\text{pV = nRT}}$
${\text{p}}$is the pressure
V is the volume
${\text{n}}$ is the number of moles of ideal gas
R is the gas constant
T is the temperature
We will convert the temperature from ${\text{20}}{\,^{\text{o}}}{\text{C}}$ to kelvin as follows:
${\text{20}}{\,^{\text{o}}}{\text{C}}\,{\text{ + }}\,{\text{273}}\,{\text{ = }}\,{\text{293K}}$
We will rearrange the ideal gas equation for volume of the gas as follows:
${\text{V}}\,{\text{ = }}\,\dfrac{{{\text{nRT}}}}{{\text{p}}}$
On substituting $8.34 \times {10^{ - 3}}$ for n, $0.0831\,{\text{L}}\,{\text{bar}}\,{{\text{K}}^{ - 1}}{\text{mo}}{{\text{l}}^{ - 1}}$ for R, ${\text{293K}}$for T, and $1$bar for pressure,
${\text{V}}\,{\text{ = }}\,\dfrac{{8.34 \times {{10}^{ - 3}}\,{\text{mol}}\, \times 0.0831\,{\text{L}}\,{\text{bar}}\,{{\text{K}}^{ - 1}}{\text{mo}}{{\text{l}}^{ - 1}} \times {\text{293K}}}}{{1{\text{bar}}}}$
${\text{V}}\,{\text{ = }}\,0.203\,{\text{L}}$
So, $0.203\,{\text{L}}$ of dihydrogen at ${\text{20}}{\,^{\text{o}}}{\text{C}}$ and one bar will be released when $0.15$ g of aluminium reacts with caustic soda.

Therefore, $0.203\,{\text{L}}$is the correct answer.

Note: The sodium hydroxide is known as caustic soda. The value of gas constant R differ in different units so, the units of pressure, volume and temperature are important. Molar mass of a monatomic element is equal to the atomic mass. For stoichiometric comparison generally the mole comparison a chemical balanced equation is very important. Drain cleaner, drainex is used to clean the blocked sewer pipes contains small bits of aluminium and caustic soda.