Problem 49 - A Complete Resource Book in Chemistry for JEE Main

Question

The equivalent conductance at infinite dilution of \(\mathrm{HCl}\) and \(\mathrm{NaCl}\) are \(426.15\) and \(126.15 \mathrm{mho} \mathrm{cm}^{2} \mathrm{~g} \mathrm{eq}^{-1}\) respectively. It can be said that the mobility of (a) \(\mathrm{H}^{+}\)ions is much more than that of \(\mathrm{Cl}\) ions (b) \(\mathrm{Cl}\) - ions is much more than that of \(\mathrm{H}^{+}\)ions (c) \(\mathrm{H}^{+}\)ions is much more than that of \(\mathrm{Na}^{+}\)ions (d) \(\mathrm{Na}^{+}\)ions is much more than that of \(\mathrm{H}^{+}\)ions

Step-by-Step Solution

Answer

Option (c): \(\text{H}^+\) ions have much greater mobility than \(\text{Na}^+\) ions.

Step 1: Understanding Equivalent Conductance

The equivalent conductance values represent the conductive ability of ions at infinite dilution. The larger the equivalent conductance, the higher the mobility of the ions contributing to it.

Step 2: Comparing Equivalent Conductance of \(\text{HCl}\) and \(\text{NaCl}\)

The equivalent conductance of \(\text{HCl}\) is \(426.15\) mho cm\(^{2}\) g eq\(^{-1}\) and that of \(\text{NaCl}\) is \(126.15\) mho cm\(^{2}\) g eq\(^{-1}\). The difference in these values is attributed to the mobility difference between \(\text{H}^{+}\) and \(\text{Na}^{+}\) ions.

Step 3: Analyzing Ion Mobility

The higher value for \(\text{HCl}\) suggests that \(\text{H}^+\) ions have much larger mobility than \(\text{Cl}^–\) ions, which are common to both salts.Additionally, since \(\text{NaCl}\) has a smaller conductance compared to \(\text{HCl}\), \(\text{H}^{+}\) ions must have greater mobility than \(\text{Na}^{+}\) ions.

Step 4: Conclusion

Therefore, the mobility of \(\text{H}^+\) ions is much more than that of \(\text{Na}^+\) ions.

Key Concepts

Ion Mobility

Ion mobility refers to the ease with which an ion moves through a medium when an electric field is applied. The mobility of an ion is determined by several factors, including its charge, size, and the viscosity of the medium. In simple terms, this is how fast or slow an ion can travel through a solution. For example, when comparing ions, smaller ions or ions with a higher charge tend to be more mobile. This is because they encounter less resistance as they travel.
For instance, hydrogen ions ( H^{+} ) tend to have a high mobility due to their small size and high charge density, allowing them to pass through the medium quickly. On the other hand, larger ions, or those with less charge, such as sodium ions ( Na^{+} ), typically move more slowly.

HCl Conductance

HCl conductance is essentially the measurement of how well hydrochloric acid (HCl) conducts electricity in a solution. The conductance of HCl is significantly high, which is indicated by its equivalent conductance at infinite dilution being 426.15 mho cm\(^2\) g eq\(^{-1}\). This high value reflects the high mobility of the H^{+} ion in HCl solutions.

• H^{+} ions move very rapidly because they can quickly jump from one water molecule to another, thanks to the Grotthuss mechanism.
• This means, in solutions, H^{+} ions contribute significantly to the electrical conductance.

Due to its smaller size and the ability to interact efficiently with water molecules, HCl tends to show excellent conductance in solutions.

NaCl Conductance

NaCl conductance relates to how well sodium chloride (NaCl) can conduct electricity in a solution. Compared to HCl, NaCl has a lower equivalent conductance at infinite dilution, measured at 126.15 mho cm\(^2\) g eq\(^{-1}\). This conductance is influenced by both the Na^{+} and Cl^{-} ions in the solution.

• The Cl^{-} ion contributes to the conductance, but its mobility is lower compared to H^{+} ions.
• The Na^{+} ion also plays a role, but it moves substantially slower than H^{+} ions due to its larger size and lower charge density.

Consequently, even though NaCl conducts electricity, it does so less effectively than HCl, primarily due to the slower movement of its constituent ions.

Ionic Conductivity in Solutions

Ionic conductivity in solutions refers to the ability of dissolved ions to conduct electricity. This property is essential in many applications, such as electrochemistry, battery design, and chemical analysis. The conductivity of a solution depends on several key factors:

• Type of ions present: Smaller, highly charged ions tend to enhance conductivity more than larger, less charged ions.
• Concentration of ions: More ions in a solution generally lead to higher conductivity, although this effect is more pronounced at lower concentrations.
• Temperature: Higher temperatures usually increase ion mobility by reducing the solution's viscosity, thus improving conductivity.

Understanding how ions like H^{+} or Na^{+} contribute differently to conductivity helps explain why substances like HCl have higher equivalent conductance values compared to NaCl . This knowledge is crucial for predicting and controlling the behavior of ionic solutions in practical scenarios.