Question

A \(0.036 M\) aqueous nitrous acid \(\left(\mathrm{HNO}_{2}\right)\) solution has an osmotic pressure of 0.93 atm at \(25^{\circ} \mathrm{C}\). Calculate the percent ionization of the acid.

Short answer

The percent ionization of the acid is 5%.

Step-by-step solution

Understand Osmotic Pressure Equation

The osmotic pressure (\( \Pi \)) for a solution can be calculated using the equation \( \Pi = iMRT \), where \( i \) is the van't Hoff factor, \( M \) is the molarity, \( R \) is the ideal gas constant (0.0821 L atm/mol K), and \( T \) is the temperature in Kelvin. We need to re-arrange this formula to solve for the van't Hoff factor,\( i \).

Convert Temperature to Kelvin

Convert the temperature from Celsius to Kelvin. \( 25^{\circ} \mathrm{C} \) is \( 298 \mathrm{K} \).

Calculate van't Hoff Factor

Substitute the values into the osmotic pressure equation to solve for \( i \). Given that osmotic pressure \( \Pi = 0.93 \text{ atm} \), molarity \( M = 0.036 \text{ M} \), the temperature \( T = 298 \text{ K} \), and \( R = 0.0821 \text{ L atm/mol K} \), we have:\[0.93 = i \times 0.036 \times 0.0821 \times 298.\]Thus, \( i = \frac{0.93}{0.036 \times 0.0821 \times 298} \approx 1.05.\)

Understand van't Hoff Factor for Ionization

The van't Hoff factor, \( i \), is related to the degree of ionization. For a weak acid that partially ionizes, \( i \) is slightly more than 1. If the acid ionizes by \( \alpha \) fraction, \( i = 1 + \alpha,\) since the acid turns into \( H^+ \) and \( NO_2^- \) ions.

Calculate Percent Ionization

Using \( i = 1 + \alpha, \) we find \( \alpha = i - 1 = 1.05 - 1 = 0.05. \) The percent ionization is \( \alpha \times 100\% = 0.05 \times 100\% = 5\%. \)

Key concepts

Osmotic Pressure

Osmotic pressure is a vital concept in chemistry, describing the pressure required to stop the flow of solvent molecules through a semipermeable membrane. It's directly related to the concentration of solute particles in a solution. The formula for calculating osmotic pressure, \( \Pi = iMRT \), involves the van’t Hoff factor (\( i \)), molarity (\( M \)), the ideal gas constant (\( R \)), and the temperature (\( T \)) in Kelvin.

Osmotic pressure depends on the number of solute particles, meaning it can tell us about ionization in weak acids. A higher osmotic pressure indicates more ionization, as more solute particles are created.

Knowing how to rearrange and solve this equation helps us understand key characteristics of solutions, like the extent to which a weak acid ionizes in a solvent.

Van't Hoff Factor

The van’t Hoff factor, denoted \( i \), represents the number of particles a solute produces in solution. This factor increases in value when a compound dissociates into ions.

For weak acids, which do not completely dissociate, the van’t Hoff factor is slightly greater than 1. This slight increase reflects the partial ionization that occurs, resulting in additional ions beyond the original solute.

In our example with nitrous acid, the calculated van’t Hoff factor of approximately 1.05 suggests that the acid ionizes only to a small extent in water. This interpretation of \( i \) gives insight into the solution's behavior and properties, further linking it to concepts like osmotic pressure and percent ionization.

Weak Acid Ionization

Weak acids like nitrous acid partially dissociate in solution, producing a small proportion of ions compared to strong acids. This limited ionization is measurable and essential in understanding weak acid behavior.

Ionization of a weak acid is expressed via the equilibrium constant or the degree of ionization. The degree of ionization tells us what fraction of the weak acid has ionized, indicated by \( \alpha \).

• When \( \alpha \) is small, it means less ionization.
• In our scenario, \( \alpha = 0.05 \), indicating 5% of the nitrous acid molecules ionize in solution.

Understanding this process helps in solving problems involving weak acids and allows us to predict how the solution will behave under different conditions, such as changes in concentration or temperature.

Nitrous Acid

Nitrous acid, with the chemical formula \( \text{HNO}_2 \), is a weak acid known for its unstable properties in water. It's an essential compound connected to various chemical reactions, including diazotization in organic synthesis.

In aqueous solutions, nitrous acid only partially ionizes, producing \( ext{H}^+ \) and \( ext{NO}_2^- \) ions. This incomplete ionization makes it an excellent example for studying weak acid behavior.

• Relatively low ionization percentage highlights nitrous acid's weak acidic nature.
• It's commonly used in the lab owing to its specific reaction characteristics.

Understanding nitrous acid’s behavior in solution gives broader insights into the nature of weak acids, helping you grasp concepts like ionization, osmotic pressure, and the van't Hoff factor.