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Calculate the osmotic pressure of each of the following aqueous solutions at \(20^{\circ} \mathrm{C}:\) a. \(2.39 M\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) b. \(9.45 \mathrm{mM} \mathrm{MgCl}_{2}\) c. \(40.0 \mathrm{mL}\) of glycerol \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) in \(250.0 \mathrm{mL}\) of aqueous solution (density of glycerol \(=1.265 \mathrm{g} / \mathrm{mL}\) ) d. \(25 \mathrm{g}\) of \(\mathrm{CaCl}_{2}\) in \(350 \mathrm{mL}\) of solution

Short Answer

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Question: Calculate the osmotic pressures for the following solutions at 20掳C: a. 2.39 M methanol (CH3OH) solution b. 9.45 mM MgCl鈧 solution c. 40.0 mL of glycerol (C鈧僅鈧圤鈧) in 250.0 mL of aqueous solution (density of glycerol = 1.265 g/mL) d. 25 g CaCl鈧 in 350 mL solution Answer: a. The osmotic pressure of the 2.39 M methanol solution is 56.63 atm. b. The osmotic pressure of the 9.45 mM MgCl鈧 solution is 0.686 atm. c. The osmotic pressure of the glycerol solution is 72.09 atm. d. The osmotic pressure of the CaCl鈧 solution is 46.53 atm.

Step by step solution

01

Convert temperature to Kelvin

First, we need to convert the given temperature in Celsius to Kelvin by adding 273.15. Temperature in Kelvin = 20掳C + 273.15 = 293.15 K
02

Determine the number of moles

Now, we will find the number of moles in 1 L of the given solution: Number of moles (n) = 2.39 M 脳 1 L = 2.39 mol
03

Calculate the osmotic pressure

Using the formula 螤 = nRTC/V and plugging in the values, we get: 螤 = (2.39 mol)(0.0821 L atm mol鈦宦 K鈦宦)(293.15 K) / 1 L = 56.63 atm The osmotic pressure of the 2.39 M methanol solution is 56.63 atm. #b. 9.45 mM MgCl鈧 solution#
04

Convert temperature to Kelvin

As before, we need to convert the given temperature in Celsius to Kelvin by adding 273.15. Temperature in Kelvin = 20掳C + 273.15 = 293.15 K
05

Determine the number of moles

First, convert the concentration from mM to M by dividing by 1000: 9.45 mM = 9.45 x 10鈦宦 M Now, we will find the number of moles in 1 L of the given solution: Number of moles (n) = 9.45 x 10鈦宦 M 脳 1 L = 9.45 x 10鈦宦 mol Note that MgCl鈧 dissociates into three ions (Mg虏鈦 and 2 Cl鈦) in a solution. Hence, it contributes three times the number of moles of solute in the solution: Total moles of solute = 3 脳 (9.45 x 10鈦宦 mol) = 28.35 x 10鈦宦 mol
06

Calculate the osmotic pressure

Using the formula 螤 = nRTC/V and plugging in the values, we get: 螤 = (28.35 x 10鈦宦 mol)(0.0821 L atm mol鈦宦 K鈦宦)(293.15 K) / 1 L = 0.686 atm The osmotic pressure of the 9.45 mM MgCl鈧 solution is 0.686 atm. #c. 40.0 mL of glycerol (C鈧僅鈧圤鈧) in 250.0 mL of aqueous solution (density of glycerol = 1.265 g/mL)#
07

Convert temperature to Kelvin

As before, we need to convert...
08

Determine the number of moles

First, we need to find the mass of glycerol in the solution: Mass of glycerol = (volume of glycerol) * (density) = (40.0 mL) * (1.265 g/mL) = 50.6 g Now, we'll find the moles of glycerol: Moles of glycerol = mass of glycerol / molar mass = 50.6 g / 92.09 g mol鈦宦 = 0.549 mol
09

Calculate the osmotic pressure

Our solution volume is 250.0 mL, so we'll convert it to liters: Volume of solution = 250.0 mL 脳 (1 L / 1000 mL) = 0.250 L Now, we'll use the formula 螤 = nRTC/V and plug in the values: 螤 = (0.549 mol)(0.0821 L atm mol鈦宦 K鈦宦)(293.15 K) / 0.250 L = 72.09 atm The osmotic pressure of the glycerol solution is 72.09 atm. #d. 25 g CaCl鈧 in 350 mL solution#
10

Convert temperature to Kelvin

As before, we need to convert...
11

Determine the number of moles

First, let's find the moles of CaCl鈧 in the solution: Moles of CaCl鈧 = mass of CaCl鈧 / molar mass = 25 g / 110.98 g mol鈦宦 = 0.225 mol As CaCl鈧 dissociates into three ions (Ca虏鈦 and 2 Cl鈦) in the solution, it contributes three times the number of moles of solute in the solution: Total moles of solute = 3 脳 (0.225 mol) = 0.675 mol
12

Calculate the osmotic pressure

Our solution volume is 350.0 mL, so we'll convert it to liters: Volume of solution = 350.0 mL 脳 (1 L / 1000 mL) = 0.350 L Now, we'll use the formula 螤 = nRTC/V and plug in the values: 螤 = (0.675 mol)(0.0821 L atm mol鈦宦 K鈦宦)(293.15 K) / 0.350 L = 46.53 atm The osmotic pressure of the CaCl鈧 solution is 46.53 atm.

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Key Concepts

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

Colligative Properties
Understanding colligative properties is crucial for solving osmotic pressure calculations. Essentially, colligative properties are characteristics of solutions that depend on the number of solute particles, irrespective of their nature, in a given amount of solvent. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

Osmotic pressure, specifically, is a colligative property that reflects the pressure required to prevent the movement of solvent molecules through a semipermeable membrane. It's influenced by multiple factors, one of which is solute concentration鈥攎easured in terms like molarity (M). When dealing with dissociative compounds like MgCl鈧 and CaCl鈧, you must account for the ionization, as each unit of solute can produce multiple particles, thus having a greater effect on osmotic pressure.

To correctly solve osmotic pressure problems, it's vital to acknowledge that the presence of each additional particle from dissolution and ionization can significantly alter the results, and this plays a critical role in the equations we use in calculations.
Molarity and Molality
When working with solutions, it's important to understand the difference between molarity and molality, as both measure solute concentration. Molarity (M) is defined as the number of moles of solute per liter of solution. This concentration unit is temperature-dependent since it involves volume, which can change with temperature. On the other hand, molality (m) is the number of moles of solute per kilogram of solvent and is not affected by temperature.

In osmotic pressure calculations, we typically use molarity because the equations are based on the volume of the solution. The nuances in converting from molarity to molality or handling units like millimolar (mM) can sway the computed osmotic pressure, making a profound understanding of these concepts imperative for students solving chemistry problems.
Dissolution and Ionization
The process of dissolution involves the breaking down of a solute in a solvent to form a solution. Upon dissolution, some compounds may undergo ionization, particularly ionic salts like MgCl鈧 and CaCl鈧, where they split into individual ions. For instance, MgCl鈧 dissociates into Mg虏鈦 and two Cl鈦 ions.

When calculating osmotic pressure, each ion contributes to the overall number of particles in the solution. Hence, a 1 molar (1 M) solution of MgCl鈧 does not simply have a 1:1 ratio of solute to solvent. Instead, it contributes thrice as many particles due to ionization. This amplifies the colligative effects and, thus, the osmotic pressure. Recognizing the number of particles generated per formula unit of the solute through dissolution and ionization is essential in colligative property calculations.
Solutions and Solubility
The concept of solutions and solubility is fundamental to understanding osmotic pressure. A solution is a homogeneous mixture comprising one or more solutes dissolved in a solvent. Solubility indicates the extent to which a solute can dissolve in a given solvent at a specific temperature and pressure.

Factors like temperature and the nature of both the solute and solvent impact solubility. When solutes dissolve, they increase the solution's osmotic pressure proportionately to their concentration. For non-electrolytes like methanol and glycerol, which do not dissociate into ions, the impact on osmotic pressure is direct and only based on the number of moles dissolved. Contrastively, for electrolytes that disassociate, like MgCl鈧 or CaCl鈧, the resulting ions each exert their effect on the osmotic pressure. It's important for students to discern between these types of solutes to accurately perform osmotic pressure calculations.

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