Rank The Following Aqueous Solutions In Order Of Electrical Conductivity

Electrical conductivity in aqueous solutions is a fascinating phenomenon governed by the concentration and mobility of ions. Ranking aqueous solutions based on their electrical conductivity requires a nuanced understanding of several factors, including the nature of the solute, its degree of dissociation, and the resulting ion concentrations. This article provides a comprehensive guide to understanding and ranking aqueous solutions by their electrical conductivity.

Understanding Electrical Conductivity in Aqueous Solutions

Electrical conductivity, often represented by the symbol σ (sigma), is a measure of a material's ability to conduct electric current. In aqueous solutions, this conductivity is primarily determined by the presence and mobility of ions. These ions act as charge carriers, facilitating the flow of electricity through the solution.

Several key factors influence the electrical conductivity of aqueous solutions:

• Concentration of Ions: Higher ion concentrations generally lead to greater conductivity, as more charge carriers are available.
• Charge of Ions: Ions with higher charges (e.g., $Al^{3+}$ compared to $Na^+$) contribute more significantly to conductivity.
• Mobility of Ions: Smaller, less hydrated ions tend to be more mobile and thus contribute more to conductivity.
• Degree of Dissociation: Strong electrolytes dissociate completely in water, producing a large number of ions, while weak electrolytes only partially dissociate.
• Temperature: Higher temperatures typically increase conductivity by enhancing ion mobility.

Strong vs. Weak Electrolytes

A critical distinction in aqueous solutions is between strong and weak electrolytes.

• Strong Electrolytes: These substances dissociate almost completely into ions when dissolved in water. Examples include strong acids (e.g., hydrochloric acid, HCl), strong bases (e.g., sodium hydroxide, NaOH), and most salts (e.g., sodium chloride, NaCl).
• Weak Electrolytes: These substances only partially dissociate into ions in water. Examples include weak acids (e.g., acetic acid, $CH_3COOH$), weak bases (e.g., ammonia, $NH_3$), and some sparingly soluble salts.

The degree of dissociation, often represented by the dissociation constant (K), plays a pivotal role in determining the ion concentration and, consequently, the electrical conductivity of the solution.

Factors Affecting Ion Mobility

Ion mobility is another crucial factor affecting electrical conductivity. Several factors influence how quickly ions can move through a solution:

• Ionic Size: Smaller ions generally have higher mobility because they experience less hydrodynamic drag.
• Charge Density: Ions with lower charge density (charge distributed over a larger volume) tend to be more mobile.
• Hydration: Ions in aqueous solution are surrounded by water molecules in a process called hydration. Highly hydrated ions are larger and move more slowly.

Temperature Dependence

The electrical conductivity of aqueous solutions typically increases with temperature. This is because higher temperatures increase the kinetic energy of the ions, allowing them to move more freely through the solution. Temperature also affects the viscosity of the solvent, which can impact ion mobility.

Ranking Aqueous Solutions by Electrical Conductivity: A Step-by-Step Approach

To rank aqueous solutions by their electrical conductivity, consider the following steps:

1. Identify the Solute: Determine the chemical formula and nature of the solute in each solution.
2. Determine Electrolyte Strength: Classify each solute as a strong or weak electrolyte. Strong electrolytes dissociate completely, while weak electrolytes only partially dissociate.
3. Determine Ion Concentrations: Estimate the ion concentrations in each solution based on the solute concentration and degree of dissociation.
4. Consider Ion Charges: Note the charges of the ions produced by each solute. Higher charges contribute more to conductivity.
5. Evaluate Ion Mobility: Consider the relative sizes and hydration of the ions. Smaller, less hydrated ions are more mobile.
6. Account for Temperature: If the solutions are at different temperatures, adjust the estimated conductivity accordingly.
7. Rank the Solutions: Based on the above factors, rank the solutions in order of increasing electrical conductivity.

Case Studies: Ranking Different Aqueous Solutions

Let's apply this approach to several examples to illustrate how to rank aqueous solutions by electrical conductivity.

Example 1: Comparing NaCl, KCl, and $MgCl_2$ Solutions

Consider three aqueous solutions, each with a concentration of 0.1 M:

• 0. 1 M NaCl (Sodium Chloride)
• 1. 1 M KCl (Potassium Chloride)
• 2. 1 M $MgCl_2$ (Magnesium Chloride)

Step 1: Identify the Solutes

• NaCl, KCl, $MgCl_2$

Step 2: Determine Electrolyte Strength

All three are strong electrolytes and dissociate completely in water.

Step 3: Determine Ion Concentrations

• 0. 1 M NaCl → 0.1 M $Na^+$ + 0.1 M $Cl^-$ (Total ion concentration: 0.2 M)
• 1. 1 M KCl → 0.1 M $K^+$ + 0.1 M $Cl^-$ (Total ion concentration: 0.2 M)
• 2. 1 M $MgCl_2$ → 0.1 M $Mg^{2+}$ + 0.2 M $Cl^-$ (Total ion concentration: 0.3 M)

Step 4: Consider Ion Charges

• NaCl and KCl produce singly charged ions ($Na^+$, $K^+$, $Cl^-$).
• $MgCl_2$ produces one doubly charged ion ($Mg^{2+}$) and two singly charged ions ($Cl^-$).

Step 5: Evaluate Ion Mobility

• The mobility of $K^+$ is slightly higher than $Na^+$ due to its larger size and lower charge density, resulting in less hydration.
• $Mg^{2+}$ has a higher charge density and is more hydrated than $Na^+$ or $K^+$, reducing its mobility.

Step 6: Account for Temperature

Assume all solutions are at the same temperature.

Step 7: Rank the Solutions

Considering the ion concentrations, charges, and mobilities:

1. $MgCl_2$: Highest conductivity due to the highest total ion concentration (0.3 M) and the presence of the doubly charged $Mg^{2+}$ ion.
2. KCl: Higher conductivity than NaCl due to the slightly greater mobility of $K^+$ compared to $Na^+$.
3. NaCl: Lowest conductivity due to lower ion mobility compared to KCl and lower total ion concentration and charge compared to $MgCl_2$.

Therefore, the ranking in order of increasing electrical conductivity is:

NaCl < KCl < $MgCl_2$

Example 2: Comparing HCl, $CH_3COOH$, and NaCl Solutions

Consider three aqueous solutions, each with a concentration of 0.1 M:

• 0. 1 M HCl (Hydrochloric Acid)
• 1. 1 M $CH_3COOH$ (Acetic Acid)
• 2. 1 M NaCl (Sodium Chloride)

Step 1: Identify the Solutes

• HCl, $CH_3COOH$, NaCl

Step 2: Determine Electrolyte Strength

• HCl and NaCl are strong electrolytes.
• $CH_3COOH$ is a weak electrolyte.

Step 3: Determine Ion Concentrations

• 0. 1 M HCl → 0.1 M $H^+$ + 0.1 M $Cl^-$ (Total ion concentration: 0.2 M)
• 1. 1 M $CH_3COOH$ ⇌ 0. 0013 M $H^+$ + 0. 0013 M $CH_3COO^-$ (Total ion concentration: ~0.0026 M; Ka ≈ 1.8 x $10^{-5}$)
• 2. 1 M NaCl → 0.1 M $Na^+$ + 0.1 M $Cl^-$ (Total ion concentration: 0.2 M)

Step 4: Consider Ion Charges

All ions are singly charged.

Step 5: Evaluate Ion Mobility

• $H^+$ has exceptionally high mobility due to its unique proton-hopping mechanism in water.
• $Cl^-$ has relatively high mobility.
• $Na^+$ has moderate mobility.
• $CH_3COO^-$ has relatively low mobility due to its larger size.

Step 6: Account for Temperature

Assume all solutions are at the same temperature.

Step 7: Rank the Solutions

Considering the ion concentrations, charges, and mobilities:

1. HCl: Highest conductivity due to high ion concentration and the exceptionally high mobility of $H^+$.
2. NaCl: Significantly higher conductivity than $CH_3COOH$ because it is a strong electrolyte.
3. $CH_3COOH$: Lowest conductivity due to its weak electrolyte nature, resulting in a very low ion concentration.

Therefore, the ranking in order of increasing electrical conductivity is:

$CH_3COOH$ < NaCl < HCl

Example 3: Comparing $H_2SO_4$, KOH, and $NH_3$ Solutions

Consider three aqueous solutions, each with a concentration of 0.1 M:

• 0. 1 M $H_2SO_4$ (Sulfuric Acid)
• 1. 1 M KOH (Potassium Hydroxide)
• 2. 1 M $NH_3$ (Ammonia)

Step 1: Identify the Solutes

• $H_2SO_4$, KOH, $NH_3$

Step 2: Determine Electrolyte Strength

• $H_2SO_4$ is a strong acid (strong electrolyte).
• KOH is a strong base (strong electrolyte).
• $NH_3$ is a weak base (weak electrolyte).

Step 3: Determine Ion Concentrations

• 0. 1 M $H_2SO_4$ → 0.1 M $SO_4^{2-}$ + 0. 1 M $H^+$ (first dissociation is complete) Total ion concentration: ~0.3 M (considering only the first dissociation)
• 1. 1 M KOH → 0.1 M $K^+$ + 0.1 M $OH^-$ (Total ion concentration: 0.2 M)
• 2. 1 M $NH_3$ + $H_2O$ ⇌ ~0.0013 M $NH_4^+$ + ~0.0013 M $OH^-$ (Total ion concentration: ~0.0026 M; Kb ≈ 1.8 x $10^{-5}$)

Step 4: Consider Ion Charges

• $H_2SO_4$ produces one doubly charged ion ($SO_4^{2-}$) and one singly charged ion ($H^+$).
• KOH produces singly charged ions ($K^+$ and $OH^-$).
• $NH_3$ produces singly charged ions ($NH_4^+$ and $OH^-$).

Step 5: Evaluate Ion Mobility

• $H^+$ has exceptionally high mobility.
• $K^+$ has relatively high mobility.
• $OH^-$ has relatively high mobility.
• $SO_4^{2-}$ has moderate mobility.
• $NH_4^+$ has moderate mobility.

Step 6: Account for Temperature

Assume all solutions are at the same temperature.

Step 7: Rank the Solutions

Considering the ion concentrations, charges, and mobilities:

1. $H_2SO_4$: Likely the highest conductivity due to the higher total ion concentration (considering both dissociations) and the presence of the doubly charged $SO_4^{2-}$ ion and the highly mobile $H^+$.
2. KOH: Significantly higher conductivity than $NH_3$ because it is a strong electrolyte.
3. $NH_3$: Lowest conductivity due to its weak electrolyte nature, resulting in a very low ion concentration.

Therefore, the ranking in order of increasing electrical conductivity is:

$NH_3$ < KOH < $H_2SO_4$

Advanced Considerations

Several advanced factors can further influence the electrical conductivity of aqueous solutions.

• Ionic Strength: The ionic strength of a solution is a measure of the total concentration of ions in the solution. Higher ionic strength can affect ion mobility and activity coefficients, influencing conductivity.
• Ion Pairing: In concentrated solutions, ions of opposite charges can associate to form ion pairs, reducing the effective ion concentration and conductivity.
• Complex Formation: Some ions can form complexes with other species in solution, which can affect their charge and mobility.
• Solvent Effects: The nature of the solvent can also influence ion mobility and conductivity. For example, solvents with higher dielectric constants tend to better support ion dissociation.

Practical Applications

Understanding and manipulating the electrical conductivity of aqueous solutions has numerous practical applications in various fields.

• Electrochemistry: Electrochemical processes, such as electroplating, electrolysis, and battery operation, rely heavily on the electrical conductivity of electrolyte solutions.
• Environmental Monitoring: Conductivity measurements are used to assess water quality, monitor pollution levels, and detect changes in salinity.
• Chemical Analysis: Conductivity measurements can be used to determine the concentration of ions in solution, monitor chemical reactions, and characterize electrolyte solutions.
• Biological Systems: Electrical conductivity plays a crucial role in biological systems, such as nerve impulse transmission, muscle contraction, and ion transport across cell membranes.

Conclusion

Ranking aqueous solutions by electrical conductivity requires a comprehensive understanding of the factors that influence ion concentration and mobility. Strong electrolytes, higher ion charges, and smaller, less hydrated ions generally lead to higher conductivity. By systematically analyzing the solutes, their dissociation behavior, and the resulting ion characteristics, it is possible to accurately predict and rank the electrical conductivity of different aqueous solutions. This knowledge is invaluable in a wide range of scientific, industrial, and environmental applications, where precise control and understanding of electrical conductivity are essential.