1. A bottle of H2SO4 (d = 1.787 gm/ml) is labelled 86% by mass. What is the molarity of the solution? What volume of the acid is required to make 1 Litre of 0.2 M H2SO4.

To solve the problem of finding the molarity of an 86% by mass sulfuric acid solution and determining the volume needed to prepare 1 liter of a 0.2 M solution, we can break it down into logical steps. Let’s go through this step by step.

Understanding Molarity and Mass Percentage

Molarity (M) is defined as the number of moles of solute per liter of solution. To find the molarity of the sulfuric acid (H2SO4) solution, we need to know both the density of the solution and its mass percentage.

Step 1: Calculate the mass of H2SO4 in 1 liter of solution

Given that the density (d) of the sulfuric acid solution is 1.787 g/mL, we can first find the mass of 1 liter (1000 mL) of the solution:

• Mass of solution = Volume × Density = 1000 mL × 1.787 g/mL = 1787 g

Since the solution is 86% H2SO4 by mass, we can calculate the mass of H2SO4 in this solution:

• Mass of H2SO4 = 0.86 × 1787 g = 1537.82 g

Step 2: Calculate the number of moles of H2SO4

Next, we need to convert the mass of H2SO4 into moles. The molar mass of H2SO4 is approximately 98.08 g/mol. Thus, the number of moles can be calculated as follows:

• Moles of H2SO4 = Mass / Molar Mass = 1537.82 g / 98.08 g/mol ≈ 15.66 mol

Step 3: Calculate the molarity of the solution

Now that we have the number of moles in 1 liter of solution, we can determine the molarity:

• Molarity (M) = Moles of solute / Volume of solution (L) = 15.66 mol / 1 L = 15.66 M

Preparing a 0.2 M Solution

Now that we know the molarity of the concentrated sulfuric acid solution, we want to find out how much of this concentrated solution is needed to prepare 1 liter of a 0.2 M H2SO4 solution.

Step 1: Use the dilution equation

The dilution equation is given by:

• C1V1 = C2V2

Where:

• C1 = initial concentration (15.66 M)
• V1 = volume of concentrated solution needed
• C2 = final concentration (0.2 M)
• V2 = final volume of the diluted solution (1 L)

Step 2: Solve for V1

Now, substituting the known values into the equation:

• 15.66 M × V1 = 0.2 M × 1 L
• V1 = (0.2 M × 1 L) / 15.66 M ≈ 0.01276 L

Converting this to milliliters:

• V1 ≈ 0.01276 L × 1000 mL/L ≈ 12.76 mL

Summary of Findings

To summarize:

• The molarity of the 86% H2SO4 solution is approximately 15.66 M.
• To prepare 1 liter of a 0.2 M H2SO4 solution, you will need about 12.76 mL of the concentrated sulfuric acid solution.

This method highlights the importance of understanding concentration, dilution, and precise calculations when working with chemical solutions. If you have any further questions about this or related topics, feel free to ask!