Problem 82 - Chemistry The Central Science

Question

A dilute aqueous solution of an organic compound soluble in water is formed by dissolving 2.35 g of the compound in water to form 0.250 L of solution. The resulting solution has an osmotic pressure of 0.605 atm at \(25^{\circ} \mathrm{C}\) . Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

Step-by-Step Solution

Answer

The molar mass of the organic compound is approximately 378.71 g/mol.

Step 1: List the given information

We are given the following information: - Mass of organic compound = 2.35 g - Volume of solution = 0.250 L - Osmotic pressure = 0.605 atm - Temperature = 25°C (298.15 K)

Step 2: Write the osmotic pressure formula

The osmotic pressure (π) can be related to the concentration of the solute (moles of solute per liter of solution) using the formula: \(π = MiRT\) where: - π = osmotic pressure (atm) - M = molarity (moles of solute / L of solution) - i = van't Hoff factor (unitless), which is 1 for a nonelectrolyte - R = ideal gas constant = 0.0821 L atm K⁻¹ mol⁻¹ - T = temperature in Kelvin

Step 3: Calculate the molarity M of the solution

By rearranging the formula from step 2, we can calculate the molarity (M) of the solution: \( M = \frac{π}{iRT} \) Since the compound is a nonelectrolyte, the van't Hoff factor i will be 1. Now, we can plug in the given values: \( M = \frac{0.605 \text{ atm}}{1 \times 0.0821 \frac{\text{L atm}}{\text{K mol}} \times 298.15 \text{ K}} \) M = 0.0248 mol/L

Step 4: Calculate the moles of organic compound in the solution

Now that we know the molarity of the solution, we can calculate the number of moles of organic compound present in the solution using the formula: moles of solute = M × volume of solution moles of solute = 0.0248 mol/L × 0.250 L = 0.0062 mol

Step 5: Calculate the molar mass of the organic compound

Finally, we can determine the molar mass of the organic compound using the formula: molar mass = mass of solute / moles of solute molar mass = 2.35 g / 0.0062 mol = 378.71 g/mol So, the molar mass of the organic compound is approximately 378.71 g/mol.

Key Concepts

Molarity

Molarity is a key concept in chemistry used to express the concentration of a solution. It tells us how many moles of solute are present in one liter of solution. To find the molarity (M), you need to know the number of moles of solute and the volume of the solution in liters.
If you recall from the problem, the osmotic pressure is linked to molarity. The formula used was:

• \(\pi = MiRT\)

For this formula:- \(\pi\) represents the osmotic pressure.- \(M\) is the molarity.- \(i\) is the van't Hoff factor, which equals 1 for nonelectrolytes.- \(R\) is the ideal gas constant.- \(T\) is the temperature in Kelvin.
By rearranging the formula, we can calculate molarity with:

• \(M = \frac{\pi}{iRT}\)

This allows us to understand how concentrated the solution is, which is crucial for determining other properties such as osmotic pressure.

Nonelectrolyte

A nonelectrolyte is a substance that, when dissolved in water, does not dissociate into ions. This means it does not conduct electricity in the solution. In our example, the organic compound is assumed to be a nonelectrolyte.
This assumption simplifies our calculations. The van't Hoff factor (\(i\)) becomes 1, because there are no ions formed in the solution.
Understanding the nature of the solute as a nonelectrolyte helps in correctly applying the osmotic pressure formula. This is because the presence or absence of ions affects the calculation of molarity and impacts other properties of the solution.

Molar Mass Calculation

Molar mass is the mass of one mole of a given substance, usually expressed in g/mol. It is essential for converting between grams of a substance and the amount in moles.
To calculate the molar mass, you need both the number of moles of the substance and the mass in grams. In the exercise, after calculating the moles from the molarity and volume of the solution, we were able to determine the molar mass using this simple formula:

• molar mass = mass of solute / moles of solute

This calculation was performed as follows:

• molar mass = 2.35 g / 0.0062 mol = 378.71 g/mol

By finding the molar mass, we gain insight into the molecular scale of the compound, which can indicate its potential size and characteristics.