Question

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

Answer 1

The relation between pressure, volume, temperature and number of moles. The relation is known as the ideal gas equation or ideal gas law. This law is derived by using three laws: Charle’s law, Boyle’s law and Avogadro’s law.

Complete step by step answer:
There are three relations between pressure, volume, temperature and number of moles.
Let us talk about that.
Charles law: In this law the relation between volume and temperature is given at constant pressure and number of moles. The equation is as: At constant pressure and number of moles the volume is inversely proportional to the temperature.
Boyle’s law: In this law the relation between volume and pressure is given at constant temperature and number of moles. The equation is as: At constant temperature and number of moles the pressure is inversely proportional to the volume of the gas.
Avogadro law: In this law the relation between volume and number of moles is given at constant pressure and temperature. The relation is as: At constant pressure and temperature the volume of gas is directly proportional to the number of moles of the gas.
By using these three laws the ideal gas law is as:
$PV = nRT$ where $P$ is pressure, $V$ is the volume, $n$ is the number of moles of gas, $T$ is the temperature and $R$ is gas constant.
In this question we are given the reaction of aluminium with caustic soda. This is represented as: $2Al + 2NaOH + 2{H_2}O \to 2AlNa{O_2} + 3{H_2}$
By this reaction we can see that two moles of aluminium will form three moles of hydrogen gas. We know that one mole of aluminium has mass $27g$. Hence two moles of aluminium contains $54g$. And also one mole of hydrogen has volume $22400ml$ so for three moles volume will be as $3 \times 22400 = 67200ml$. Hence we can say that $54g$ of aluminium will generate $67.2L$ of dihydrogen. Then $0.15g$of aluminium will generate $\dfrac{{67.2}}{{54}} \times 0.15 =$ $0.1866L = 187ml$
In the question it is given that ${P_1} = {P_2} = 1atm$, ${T_1} = 273K$, ${T_2} = 20 + 273 = 293K$ and ${V_1} = 187ml$ and we have to find ${V_2}$.
By the gas law it is clear that $\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
${V_2} = \dfrac{{{P_1}{V_1}{T_2}}}{{{P_2}{T_1}}} \\\ {V_2} = \dfrac{{1 \times 187 \times 293}}{{1 \times 273}} = 200.6ml \\\ {V_2} = 201ml \\\$
So volume released will be $201ml$.

Note:
During the reaction the mass of all the substances before the reaction and after the reaction are equal i.e. mass can neither be created nor be destroyed, but can be changed from one substance to another. This is the law of conservation of mass.