Problem 132 - A Complete Resource Book in Chemistry for JEE Main

Question

When an electric current is passed through acidulated water, \(112 \mathrm{~mL}\) of hydrogen gas at NTP collects at the cathode in 965 seconds. The current passed, in ampere is (a) \(0.1\) (b) \(0.5\) (c) \(1.0\) (d) \(2.0\)

Step-by-Step Solution

Answer

The current passed is 1.0 A (option c).

Step 1: Understanding the Electrolysis

When electric current is passed through acidulated water, water decomposes into hydrogen and oxygen gas. At the cathode, hydrogen gas is produced due to the reduction of hydrogen ions.

Step 2: Using Faraday's First Law

Faraday's first law of electrolysis states that the amount of substance liberated at an electrode is directly proportional to the quantity of electricity passed. The volume of hydrogen gas at NTP can be related to the moles of gas formed and therefore to the charge passed.

Step 3: Calculating Moles of Hydrogen

At NTP (Normal Temperature and Pressure), 1 mole of any gas occupies approximately 22400 mL. Therefore, the moles of hydrogen gas collected can be calculated as: \[ \text{moles of } H_2 = \frac{112 \, \text{mL}}{22400 \, \text{mL/mol}} = 0.005 \text{ mol} \]

Step 4: Calculating Charge

Since 1 mole of hydrogen gas requires 2 Faradays (or 2 moles of electrons) for its formation, 0.005 moles of hydrogen gas requires: \[ 0.005 \, \text{mol} imes 2 \, \text{F} = 0.01 \, \text{F} \] (where 1 Faraday = 96500 C). Thus the total charge passed is: \[ Q = 0.01 \, \text{mol} \times 96500 \, \text{C/mol} = 965 \, \text{C} \]

Step 5: Calculating Current

The current \( I \) can be calculated using the formula: \[ I = \frac{Q}{t} \] where \( Q = 965 \, \text{C} \) and \( t = 965 \, \text{s} \). Thus the current is: \[ I = \frac{965 \, \text{C}}{965 \, \text{s}} = 1.0 \, \text{A} \]

Step 6: Selecting the Correct Option

From our calculations, the current is 1.0 A. Comparing with the options, the correct answer is \( 1.0 \) (option c).

Key Concepts

Electrolysis

Electrolysis is a fascinating process where chemical reactions are driven by electricity. Imagine electricity offering the power to break down compounds into simpler substances! This occurs in an electrolytic cell—a setup with two electrodes immersed in an electrolyte. The classic example is the decomposition of water. When electricity flows, water splits into its elemental gases: hydrogen and oxygen. This process underpins many modern applications, including electroplating, anodizing, and producing chemicals like chlorine.

Faraday's Laws of Electrolysis govern this process, linking the amount of electricity to the degree of reaction completion. The first law states that the mass of a substance altered at an electrode is directly proportional to the electric charge passed through the circuit.

• Mass is proportional to electricity.
• Fundamental to calculate substances produced or consumed during electrolysis.

Understanding electrolysis extends beyond theory. It explains the core principles driving electrochemical technologies, making it an essential topic in the study of chemistry and physics.

Cathode Reaction in Electrolysis

In electrolysis, the cathode plays a vital role as the electrode where reduction occurs. At this site, positively charged ions gain electrons, converting them into neutral atoms or molecules. For instance, in water electrolysis, hydrogen ions (or protons) receive electrons at the cathode to form hydrogen gas.

• Cathode: the negative electrode
• Creates neutral hydrogen from positive ions
• Essential for producing substances at the cathode

The cathode reaction can be generalized as \( ext{M}^+ + e^- \rightarrow ext{M} \), where \( ext{M}^+ \) is a positive ion and \( ext{M} \) the corresponding neutral species. This behind-the-scenes action is crucial for processes like metal reduction in electroplating and generating materials essential to various industries.

By understanding the cathode reaction, we see how electrolysis is not just separation. It’s a transformation—one that powers industries and technologies around the world.

Current Calculation in Electrolysis

Calculating current in electrolysis is a straightforward yet crucial component in understanding electrochemical processes. The current represents the flow of electric charge, calculated using the formula: \[ I = \frac{Q}{t} \]where:

• \( I \) is the current in amperes (A)
• \( Q \) is the total charge in coulombs (C)
• \( t \) is time in seconds (s)

In the context of generating hydrogen at the cathode, determining the current involves quantifying the electrons needed to form a specific volume of hydrogen gas. Faraday's laws aid us in calculating this charge \( Q \) from the moles of gas utilized in the reaction.

• Directly linked to the amount of substance produced
• Calculated from both time and charge passed

The importance of this calculation lies in its applications. Electrolysis powers a myriad of industrial processes—from refining metals to producing fuel like hydrogen. Understanding how to precisely calculate and control current is key to efficient and sustainable operations in these fields.