Question

In the electrolysis of a sodium chloride solution, what volume of ${\mathrm{H}}_2(g)$ is produced in the same time it takes to produce 257 $\mathrm{L}{\mathrm{Cl}}_2(g),$ with both volumes measured at $50{.}^{\circ }\mathrm{C}$ and 2.50 $\mathrm{atm}$ ?

Short answer

Under the given conditions of $50{.}^{\circ }\mathrm{C}$ and $2.50\mathrm{atm}$, the volume of hydrogen gas produced in the same time as 257 L of chlorine gas is also 257 L.

Step-by-step solution

Write down the balanced redox reactions and overall equation

The full balanced equation for the electrolysis of aqueous sodium chloride (NaCl) is: $2{\mathrm{Na}}^{+}+2{\mathrm{Cl}}^{-}(aq)\to 2\mathrm{Na}(s)+{\mathrm{Cl}}_2(g)$ (at the anode) $2{\mathrm{H}}_2\mathrm{O}(l)\to 2{\mathrm{OH}}^{-}+{\mathrm{H}}_2(g)$ (at the cathode) Summing these reactions: $2{\mathrm{Na}}^{+}+2{\mathrm{Cl}}^{-}+2{\mathrm{H}}_2\mathrm{O}(l)\to 2\mathrm{Na}(s)+{\mathrm{Cl}}_2(g)+2{\mathrm{OH}}^{-}+{\mathrm{H}}_2(g)$

Determine the stoichiometry of hydrogen gas and chlorine gas produced

From the balanced equation, we can see that 1 mole of hydrogen gas is produced for every mole of chlorine gas produced: $\frac{{\mathrm{moles}\mathrm{of}\mathrm{H}}_2}{{\mathrm{moles}\mathrm{of}\mathrm{Cl}}_2}=\frac{1}{1}$ If we're given the volume of ${\mathrm{Cl}}_2$, we can use this ratio to determine the volume of ${\mathrm{H}}_2$: $\frac{{\mathrm{volume}\mathrm{of}\mathrm{H}}_2}{{\mathrm{volume}\mathrm{of}\mathrm{Cl}}_2}=\frac{1}{1}$

Using the stoichiometry, find the volume of hydrogen gas

We are given the volume of chlorine gas as 257 L. Using the stoichiometry ratio from Step 2: ${\mathrm{volume}\mathrm{of}\mathrm{H}}_2={\mathrm{volume}\mathrm{of}\mathrm{Cl}}_2=257L$

Verify the given conditions are the same for both gases

To ensure the volumes of hydrogen and chlorine gases are directly comparable, verify that they are both measured at the same temperature and pressure conditions. Both gases are measured at $50{.}^{\circ }\mathrm{C}$ and $2.50\mathrm{atm}$, so the volume of hydrogen gas would also be equal to the volume of chlorine gas under these same conditions.

Conclude the answer

Under the given conditions of $50{.}^{\circ }\mathrm{C}$ and $2.50\mathrm{atm}$, the volume of hydrogen gas produced in the same time as 257 L of chlorine gas is also 257 L.

Key concepts

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are fundamental chemical processes where one substance loses electrons (oxidation) and another gains electrons (reduction). These reactions are essential in the electrolysis of sodium chloride solutions.
During the electrolysis process, ions in a solution are decomposed by an electric current. This involves both reduction and oxidation reactions occurring at different electrodes.
At the anode, which is the positive electrode, oxidation occurs. For the sodium chloride electrolysis, chlorine ions ( 2Cl^{-} ) lose electrons to form chlorine gas ( Cl_2(g) ).
At the cathode, which is the negative electrode, reduction occurs. Water molecules ( H_2O ) gain electrons to produce hydrogen gas ( H_2(g) ) and hydroxide ions ( OH^{-} ).
Understanding redox reactions is crucial, as they dictate how substances are transformed during electrolysis.

Stoichiometry

Stoichiometry is the bridge between chemical equations and real-life measurements, allowing us to calculate the quantities of reactants and products in a chemical reaction.
In our electrolysis problem, stoichiometry helps us determine the relationship between the volumes of hydrogen and chlorine gases produced.
The balanced equation shows a 1:1 mole ratio between chlorine gas and hydrogen gas, meaning for every mole of chlorine gas produced, one mole of hydrogen gas is also produced.
This mathematical relationship allows us to directly equate the volumes of gases under the same conditions of temperature and pressure, as volumetric ratios reflect molar ratios due to Avogadro's law.
With this understanding, when 257 L of chlorine gas is produced, stoichiometry tells us that 257 L of hydrogen gas is produced as well.

Chlorine Gas

Chlorine gas ( Cl_2(g) ) is a diatomic greenish-yellow gas that has significant applications in water purification, bleaching, and manufacturing.
In the context of electrolysis, chlorine gas forms at the anode. Here, chloride ions ( Cl^{-} ) from the electrolyte solution release electrons to form chlorine gas through oxidation.
This process occurs because the electric current forces the negatively charged chloride ions toward the anode, where they lose electrons.
Due to chlorine's high reactivity and its potential to form dangerous compounds, handling it requires careful control and safety measures, especially in industrial processes.

Hydrogen Gas

Hydrogen gas ( H_2(g) ) is a colorless, odorless gas that is the lightest and most abundant chemical substance in the universe.
In the electrolysis of sodium chloride solutions, hydrogen gas is produced at the cathode.
This occurs when water molecules gain electrons, undergoing reduction to form hydrogen gas and hydroxide ions ( OH^{-} ).
Hydrogen has a wide array of uses, including in fuel cells, fertilizer production, and as a clean energy source. As a crucial by-product of many industrial processes, understanding its production is vital.
Because hydrogen is highly flammable, stringent safety protocols must be in place during its industrial generation and transportation.