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Chapter 5: Problem 106

\(\mathrm{pH}\) of \(0.1 \mathrm{M}\) monobasic acid solution is found to be \(2 .\) Thus its osmotic pressure at \(\mathrm{T} . \mathrm{K}\). is (a) \(11.11 \mathrm{ST}\) (b) \(0.11 \mathrm{ST}\) (c) \(0.011 \mathrm{ST}\) (d) \(1.11 \mathrm{ST}\)

Short Answer

Expert verified
The osmotic pressure is \(0.11 \, ST\), which is option (b).

Step by step solution

01

Understand the Problem

We are given a 0.1 M solution of a monobasic acid with a pH of 2 and need to find the osmotic pressure at temperature T. K. The formula for osmotic pressure is \( \pi = iCRT \), where \( i \) is the van 't Hoff factor, \( C \) is the concentration, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.
02

Calculate the Dissociation of the Acid

Since the pH is 2, the concentration of hydrogen ions, \([H^+]\), is \(10^{-2} \; \text{M}\). For a monobasic acid, which donates one hydrogen ion, this relates directly to the degree of dissociation \(\alpha\). Thus, \( \alpha = \frac{[H^+]}{C} = \frac{10^{-2}}{0.1} = 0.1 \).
03

Calculate the van 't Hoff Factor \(i\)

The van 't Hoff factor \( i \) is used to account for particles in solution. For the ionization \( HA \rightarrow H^+ + A^- \), the effective concentration is \(1 + \alpha = 1.1 \). Hence, \( i = 1 + \alpha = 1.1 \).
04

Use the Osmotic Pressure Formula

From the equation \( \pi = i C R T \), substitute the values \(i = 1.1\), \(C = 0.1\), obtaining \( \pi = 1.1 \times 0.1 \times R T = 0.11 \, R T \).
05

Compare to Given Options

The options are given in terms of a general expression \(x \times ST\). From Step 4, we found \( \pi = 0.11 \, R T \). Assuming \(S = R\) (the universal gas constant), the expression matches option (b), which is \(0.11 \, ST\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Van 't Hoff Factor
The van 't Hoff factor, often represented by the symbol \(i\), is crucial in determining how solute particles behave in a solution. When a solute dissolves, it might dissociate into ions. The van 't Hoff factor helps us account for this dissociation by showing the number of particles the solute effectively contributes to the solution's properties.
For a simple electrolyte such as a salt, which completely dissociates, the van 't Hoff factor can be equal to the number of ions produced. For nonelectrolytes or where the dissociation is incomplete, \(i\) will be less than the number of possible ions. In the case of the monobasic acid in the exercise, the dissociation into \(H^+\) and \(A^-\) ions leads to a van 't Hoff factor of 1.1. This value indicates that the solution behaves as if there are slightly more than one molecule per dissolved unit due to the acid's partial dissociation.
Degree of Dissociation
Degree of dissociation, symbolized as \(\alpha\), helps us understand how much of a solute dissociates into ions in a solution. It is calculated by comparing the concentration of the dissociated ions to the initial concentration of the acid.
In this exercise, the initial concentration is the concentration of the monobasic acid, and the final concentration is the concentration of hydrogen ions, \(\left[H^+\right]\). Calculating \(\alpha\) involves dividing \([H^+]\) by the initial acid concentration. With \(\left[H^+\right] = 10^{-2} \; M\) and an initial concentration of 0.1 M, \(\alpha\) is calculated as 0.1, indicating that 10% of the acid dissociates into ions.
Monobasic Acid
A monobasic acid is an acid that donates only one proton (hydrogen ion, \(H^+\)) per molecule to a solution. This means it has one replaceable or ionizable hydrogen atom in its structure. The term "monobasic" comes from the Greek "mono," meaning single, and "basic," indicating the base-forming ion, which in this case is the proton.
Common examples of monobasic acids include hydrochloric acid (HCl) and nitric acid (HNO鈧�). These acids, when dissolved in water, dissociate to release one hydrogen ion. Understanding this concept is critical for calculating osmotic pressure, as it determines the initial concentration of ions produced in the solution, affecting the van 't Hoff factor.
H+ Concentration
The concentration of hydrogen ions \( [H^+] \) in a solution directly determines its acidity, as measured by pH. The relationship is encapsulated by the formula \( \text{pH} = -\log [H^+] \).
For the monobasic acid in the exercise, a pH of 2 indicates an \( [H^+] \) of \(10^{-2} \; M\). This concentration tells us how many hydrogen ions are present in a liter of solution. The derived \([H^+]\) further relates directly to the degree of dissociation \(\alpha\), which is the fraction of the acid molecules that dissociate to produce \(H^+\) ions. Understanding \( [H^+] \) helps in various calculations related to solution chemistry, including osmotic pressure and complete acid-base reactions.

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Most popular questions from this chapter

A binary liquid solution is prepared by mixing \(n\)-heptane and ethanol. Which on of the following statement is correct regarding the behavior of the solution? (a) The solution in non-ideal, showing +ve deviation from Raoult's Law. (b) The solution in non-ideal, showing \(-\) ve deviation from Raoult's Law. (c) n-heptane shows tre deviation while ethanol shows -ve deviation from Raoult's Law. (d) The solution formed is an ideal solution.

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