Question

pH of a \(0.1\) M solution of a monobasic acid is \(2.0 .\) Its osmotic pressure at a given temperature, \(T \mathrm{~K}\) is (a) \(0.1 R T\) (b) \(0.11 R T\) (c) \(0.09 R T\) (d) \(0.01 R T\)

Short answer

The osmotic pressure of the solution at temperature T is (d) 0.01 R T.

Step-by-step solution

Understanding pH in Relation to H+ Concentration

pH is a measure of the hydrogen ion concentration in a solution. The pH of a solution is calculated using the formula pH = -log [H+], where [H+] is the concentration of hydrogen ions in moles per liter (M). Given that the pH of the monobasic acid solution is 2.0, we can calculate the concentration of hydrogen ions by rearranging this equation to [H+] = 10^(-pH).

Calculate the Concentration of Hydrogen Ions

Using the rearranged pH formula, calculate the hydrogen ion concentration for the given solution: [H+] = 10^(-2.0) = 0.01 M.

Understanding Osmotic Pressure

Osmotic pressure (π) can be calculated using the formula π = i * M * R * T, where i is the van 't Hoff factor (which is 1 for a monobasic acid as it dissociates into one type of ion), M is the molarity of the solution, R is the gas constant, and T is the temperature in Kelvins.

Calculate the Osmotic Pressure

Substitute the known values into the osmotic pressure equation: π = 1 * [H+] * R * T = 0.01 * R * T.

Key concepts

pH and Hydrogen Ion Concentration

Understanding the concept of pH is crucial for students studying chemistry. The pH scale measures the acidity or basicity of a solution and ranges from 0 to 14, with 7 being neutral, values below 7 indicating acidity, and those above 7 indicating basicity. The 'p' in pH stands for 'potential' and the 'H' stands for hydrogen; thus pH is essentially a measure of the potential of the solution to attract hydrogen ions (H+).

The formula for calculating pH is simple: pH = -log[H+], where 'log' represents the logarithm to the base 10, and [H+] is the hydrogen ion concentration in moles per liter (M). To find the hydrogen ion concentration from a given pH, the formula can be inverted to [H+] = 10^(-pH).

• pH is inversely related to the hydrogen ion concentration: a low pH means high [H+], and vice versa.
• Precise control of pH is vital in many chemical and biological processes.
• Buffers are solutions that resist changes in pH upon the addition of acid or base.

Using this understanding, students can decode how the ionization of substances in solution impacts pH and drives various chemical reactions.

van 't Hoff Factor

The van 't Hoff factor (i) is a term in physical chemistry that has major implications when studying solutions. It's named after the chemist J.H. van 't Hoff who contributed significantly to the understanding of the behavior of solutions.

The factor 'i' represents the number of particles a compound dissociates into when dissolved in a solvent. For instance, common salt (NaCl), when dissolved in water, dissociates into two ions: Na+ and Cl-. Thus, its van 't Hoff factor is 2. In contrast, a monobasic acid, like the one mentioned in our problem, dissociates into only one type of ion per molecule in solution, so its van 't Hoff factor is 1.

• The van 't Hoff factor is essential when calculating properties such as boiling point elevation, freezing point depression, and osmotic pressure.
• It is important to remember that 'i' is an ideal value. Real solutions may deviate due to ion pairing or other interactions.
• In the case of non-electrolytes, substances that do not dissociate into ions, the van 't Hoff factor is typically 1.

Comprehending the van 't Hoff factor enables students to predict and calculate how dissolved substances can affect various colligative properties of a solution.

Molarity and Osmolality

When it comes to quantifying the concentration of a solution, molarity and osmolality are two crucial measurements.

Molarity (M) is one of the most commonly used units of concentration. It reflects the number of moles of a solute per liter of solution. This can be easily calculated by taking the amount (in moles) of the solute and dividing it by the volume (in liters) of the solution. Because it depends on the volume of the solution, which can change with temperature, molarity isn’t always the best measure in all circumstances.

On the other hand, osmolality measures the number of osmoles of solute particles per kilogram of solvent. It is a more precise measure when dealing with solutions that may experience temperature and pressure changes since it is based on the weight of the solvent, not the volume. Osmolality is widely utilized, especially in medical settings, to gain insight into the osmotic concentration of fluids such as blood or urine.

• Osmotic pressure calculations often use molarity (for dilute solutions) because it directly relates to the number of moles of solute particles available to exert pressure across a semipermeable membrane.
• Knowing the differences between these units of concentration allows students to accurately conduct experiments and understand their outcomes.
• It's important to choose the appropriate unit of measurement based on the chemical process or the physical conditions being studied.

Grasping these concepts provides a foundation for understanding more complex topics in chemistry, including the calculation of osmotic pressure in solutions.