25 mol of solute of molar mass 250g/mol is dissolved in 100 ml of water to obtain a solution whose density is 1.025g/mol. what is the molarity and molality of the solution ?

To calculate both the molarity and molality of the solution you're describing, we need to break down the problem into manageable steps. Let's tackle each calculation one at a time.

Understanding Molarity

Molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters. The formula for calculating molarity is:

Molarity (M) = Moles of solute / Volume of solution in liters

Step 1: Calculate Moles of Solute

You mentioned that we have 0.25 moles of solute. That's already provided, so we can move on to calculating the volume of the solution.

Step 2: Convert Volume to Liters

The volume of the solution is given as 100 mL. To convert this to liters:

• 100 mL = 100 / 1000 = 0.1 L

Step 3: Calculate Molarity

Now, we can apply the values into the molarity formula:

M = 0.25 moles / 0.1 L = 2.5 M

Exploring Molality

Next, let's determine the molality (m) of the solution. Molality is defined as the number of moles of solute per kilogram of solvent. The formula is:

Molality (m) = Moles of solute / Mass of solvent in kg

Step 1: Identify Mass of Solvent

The mass of the solvent (water) can be calculated using its volume and the density of the solution. The density of the solution is given as 1.025 g/mL. We first calculate the mass of the solution:

• Mass of solution = Density × Volume = 1.025 g/mL × 100 mL = 102.5 g

Step 2: Calculate Mass of Solvent

Next, we need to find the mass of the solvent (water). We know that:

• Mass of solute = Moles × Molar Mass = 0.25 moles × 250 g/mol = 62.5 g
• Mass of solvent = Mass of solution - Mass of solute = 102.5 g - 62.5 g = 40 g

Step 3: Convert Mass of Solvent to Kilograms

To use it in the molality formula, we convert grams to kilograms:

• 40 g = 40 / 1000 = 0.04 kg

Step 4: Calculate Molality

Now, substitute the values into the molality formula:

Molality (m) = 0.25 moles / 0.04 kg = 6.25 m

Summary of Results

To recap, for the solution you described:

• Molarity: 2.5 M
• Molality: 6.25 m

This means that the solution has a molarity of 2.5 moles per liter and a molality of 6.25 moles per kilogram of solvent. If you have any further questions or need clarification, feel free to ask!