Problem 10 - Chemistry in 30 days

Question

In the electrolysis of alkaline water, a total of \(1 \mathrm{~mol}\) of gases is evolved. The amount of water decomposed would be (a) 1 mol (b) \(2 \mathrm{~mol}\) $$ \begin{array}{llll}\text { (c) }(1 / 3) \text { mol } & \text { (d) }(2 / 3) \mathrm{mol} & \text { mol }\end{array} $$

Step-by-Step Solution

Answer

The amount of water decomposed is \(\frac{1}{3}\) mol.

Step 1: Write the Balanced Equation

The balanced chemical equation for the electrolysis of water is \(2H_2O(l) \rightarrow 2H_2(g) + O_2(g)\). This indicates that 2 moles of water produce 2 moles of hydrogen gas and 1 mole of oxygen gas, yielding a total of 3 moles of gas.

Step 2: Determine Moles of Water Decomposed

Given that a total of 1 mole of gases is evolved, we use the proportion from the balanced equation to find out how much water was decomposed. For the gases to be produced in a total amount of 1 mole, the water decomposed can be calculated as \(\frac{1}{3}\) mole, based on the total gas production ratio (2:1) from the equation.

Step 3: Verify the Calculation

Using the proportion from the balanced equation, \(2 \text{ moles of } H_2O\) produce \(3 \text{ moles of gas}\), so decomposing \(\frac{1}{3}\) mole of water must give \(\frac{3}{3} = 1\) mole of gas. This matches the given condition of evolving 1 mole of gas.

Key Concepts

Water Electrolysis

Water electrolysis is a fascinating chemical process where water is split into its constituent gases, hydrogen and oxygen, using electrical energy. It occurs in an electrolysis cell, where an electric current passes through the water, causing chemical bonds to break and form new substances. The process can be summarized by the overall chemical equation: \[ 2H_2O(l) \rightarrow 2H_2(g) + O_2(g) \]

• Two moles of liquid water decompose into two moles of hydrogen gas and one mole of oxygen gas.
• The gases are collected separately at two electrodes: hydrogen at the cathode and oxygen at the anode.
• This process is key to producing hydrogen gas, which can be used for various energy applications.

Chemical Equation Balancing

Balancing a chemical equation ensures that the numbers of each type of atom on both sides of the reaction are equal. This is grounded in the law of conservation of mass, which states that matter cannot be created or destroyed. For the electrolysis of water:

• The reactants are two molecules of water, contributing 4 hydrogen atoms and 2 oxygen atoms.
• In the products, 2 hydrogen molecules provide 4 hydrogen atoms, and an oxygen molecule provides 2 oxygen atoms.
• Thus, the atoms are balanced on both sides of the equation, confirming our balanced chemical reaction.

Mole Concept

The mole concept is fundamental in chemistry for quantifying substances. One mole is equivalent to Avogadro's number, approximately \(6.022 \times 10^{23}\) entities (like atoms or molecules). In water electrolysis:

• Electrolyzing 2 moles of water results in 3 moles of gas (2 moles of hydrogen and 1 mole of oxygen).
• If only 1 mole of gas is produced, the amount of water decomposed can be calculated by setting the proportion of decomposed water to the total gas evolved.
• Here, \(\frac{1}{3}\) mole of water decomposes to yield 1 mole of gas, as determined from the balanced equation.

Gas Evolution

Gas evolution refers to the process of gas formation and release during chemical reactions. During water electrolysis, gas evolution is a clear indicator of the reaction taking place:

• Hydrogen and oxygen gases form at different electrodes due to electric current, causing visible bubbles to appear.
• The ratio of hydrogen to oxygen is 2:1, correlating with the molecular composition of water.
• Monitoring the volume or moles of gas evolved helps understand the extent and rate of the reaction.

In the specific example provided, evolving 1 mole of gas indicates that a certain amount of water has undergone electrolysis, illustrated by the balanced equation. This understanding can be key for industries leveraging water electrolysis for sustainable hydrogen production.