Question:
What is the freezing point of a solution containing 8.1 g HBr in 100 g water, assuming that the acid to be 90% ionized?
$(K_f (H_2O) = 1.86 \,K \,kg\, mol^{-1})$
What is the freezing point of a solution containing 8.1 g HBr in 100 g water, assuming that the acid to be 90% ionized?
$(K_f (H_2O) = 1.86 \,K \,kg\, mol^{-1})$
Updated On: Jun 23, 2023
- $0.85^{\circ}C$
- $-3.8^{\circ}C$
- $-0^{\circ}C$
- $-3.5^{\circ}C$
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The Correct Option is D
Solution and Explanation
Consider the dissociation of 1 mol HBr. The degree of dissociation is 90%, i.e., $\alpha = 0.90$
$\begin{matrix}&HBr_{\left(aq\right)}&\to&H^{+}\left(aq\right)&+&Br^{-}\left(aq\right)\\ Initial\, conc.&1\, mol&&0&&0\\ Final \, conc.&1 - 0.90 = 0.10\, mol&&0.90\, mol&&0.90\, mol\end{matrix}$
$\therefore\quad$ Total number of particles $= 0.10 + 0.90 + 0.90$
$= 1.90\, mol$
van?? Hoff factor $\left(i\right) = \frac{1.90}{1.00} = 1.90$
$\Delta T_{f} = iK_{f} \frac{W_{B}}{M_{B}\cdot W_{A}} = \frac{1.90 ? 1.86 \,K\,kg\,mol^{-1} ? 8.1 \,g}{81 \,g \,mol^{-1} \times 100 \times10^{-3} \,kg}$
$= 3.5 \,K = 3.5^{\circ}C$
F.P. of solution = F.P. of solvent - depression in F.P.
$= 0^{\circ}C - 3.5^{\circ}C = -3.5^{\circ}C$
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.