Problem 23 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

A \(0.004 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is isotonic with \(0.010 \mathrm{M}\) solution of glucose at same temperature. The percentage dissociation of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is (a) \(25 \%\) (b) \(50 \%\) (c) \(75 \%\) (d) \(85 \%\)

Step-by-Step Solution

Answer

The percentage dissociation of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is \(75\%\).

Step 1: Define Isotonic Solutions

Two solutions are isotonic when they have the same osmotic pressure. To find the percentage dissociation, we need to equate the effective molar concentrations of ions and molecules in both solutions.

Step 2: Determine Glucose Osmotic Pressure Contribution

Glucose does not dissociate in solution, so its osmotic pressure is equal to its molarity. Therefore, the effective concentration contributing to osmotic pressure for glucose is \(0.010\, \mathrm{M}\).

Step 3: Express Na2SO4 Ion Contribution

Sodium sulfate (\(\mathrm{Na}_{2} \mathrm{SO}_{4}\)) dissociates in water to form three ions (two \(\mathrm{Na}^+\) ions and one \(\mathrm{SO}_{4}^{2-}\) ion). Let \(\alpha\) be the degree of dissociation. The total number of particles contributed to the solution becomes \(0.004 \times (1 + 2\alpha)\).

Step 4: Equate Isotonic Conditions

Since the solutions are isotonic, set the effective concentration from glucose equal to the particle contribution from \(\mathrm{Na}_{2} \mathrm{SO}_{4}\): \[0.010 = 0.004 \times (1 + 2\alpha)\]

Step 5: Solve for Alpha (\(\alpha\))

Solve the equation for \(\alpha\): \[0.010 = 0.004 + 0.008\alpha\]Subtract \(0.004\) from both sides: \[0.006 = 0.008\alpha\]Divide both sides by \(0.008\): \[\alpha = \frac{0.006}{0.008} = 0.75\]

Step 6: Calculate Percentage Dissociation

The percentage dissociation is calculated by multiplying \(\alpha\) by 100: \[\text{Percentage Dissociation} = 0.75 \times 100 = 75\%\]

Key Concepts

Isotonic Solutions

When two solutions are isotonic, they have equal osmotic pressure. This means that their potential to move through a semipermeable membrane is the same. As a result, there will be no net movement of solvent from one solution to the other. For a solution to be isotonic with another, like in the given exercise where a sodium sulfate solution is compared to a glucose solution, the total concentration of particles in the solution must match.

• In an isotonic scenario, despite the nature of the solute, the effective concentration, which reflects the total number of solute particles, should be identical for both solutions.
• Sodium sulfate dissociates into multiple ions in solution, thereby influencing its contribution to osmotic pressure. Conversely, glucose remains undissociated.

Understanding isotonic solutions helps in determining comparisons in real-world applications, such as medical settings where intravenous fluids must match the osmotic pressure of bodily fluids to prevent cell damage.

Osmotic Pressure

Osmotic pressure is a vital concept in chemistry and biology that determines how solutions interact with biological membranes. It is defined as the pressure required to stop the flow of solvent across a semipermeable membrane due to osmosis. This pressure depends directly on the concentration of solute particles in the solution.

• The greater the concentration of solute particles, the higher the osmotic pressure.
• In the example of glucose, its osmotic pressure equals its molarity because glucose does not ionize or dissociate in water.
• However, for ionic compounds like sodium sulfate, the osmotic pressure is determined by the total number of ions formed upon dissociation.

Understanding osmotic pressure is crucial for various applications, such as formulating isotonic drinks, medical treatments, and industrial processes that rely on fluid balance and transport.

Degree of Dissociation

The degree of dissociation denotes the fraction of a compound that separates into its ions in a solution. It is a crucial parameter in measuring the effectiveness of ionic solutions' contributions to osmotic pressure. In dissociation, compounds like sodium sulfate break down into their component ions, effectively altering the concentration of particles in a solution.

• The degree of dissociation, represented by \( \alpha \), indicates how much of the original species becomes ions.
• For sodium sulfate, which dissociates into three ions, the effective concentration contributing to osmotic pressure is modified by \(1 + 2\alpha\).
• This helps equate sodium sulfate's ion effect to glucose's non-ionizing molar contribution when determining the isotonicity.

The degree of dissociation is calculated as a percentage, revealing how much of a compound dissociates under given conditions, effectively influencing solution characteristics like conductivity and osmotic balance.