Calculate the molarity of

a.) 50.00 weight% of H2SO4 whose density is 1.31g cm-3 at 20oC

b.0 the volume of acid requires to get one litre of 0.2M acid solution

explain it clearly

To calculate the molarity of a solution, we need to understand the relationship between mass, volume, and the number of moles of solute. Let's break this down step by step for both parts of your question regarding sulfuric acid (H2SO4).

Calculating Molarity of H2SO4 Solution

First, we need to find the molarity of a 50.00 weight% H2SO4 solution with a density of 1.31 g/cm³. Molarity (M) is defined as the number of moles of solute per liter of solution.

Step 1: Determine the Mass of H2SO4 in 1 Liter of Solution

Since the density of the solution is given, we can calculate the mass of 1 liter (1000 mL) of the solution:

• Density = Mass/Volume
• Mass = Density × Volume = 1.31 g/cm³ × 1000 cm³ = 1310 g

Now, since the solution is 50.00 weight%, this means that 50.00% of the mass is H2SO4:

• Mass of H2SO4 = 50.00% of 1310 g = 0.50 × 1310 g = 655 g

Step 2: Convert Mass of H2SO4 to Moles

Next, we need to convert the mass of H2SO4 to moles. The molar mass of H2SO4 is calculated as follows:

• H: 1.01 g/mol × 2 = 2.02 g/mol
• S: 32.07 g/mol × 1 = 32.07 g/mol
• O: 16.00 g/mol × 4 = 64.00 g/mol
• Total = 2.02 + 32.07 + 64.00 = 98.09 g/mol

Now, we can find the number of moles of H2SO4:

• Moles of H2SO4 = Mass / Molar Mass = 655 g / 98.09 g/mol ≈ 6.67 moles

Step 3: Calculate Molarity

Finally, we can calculate the molarity of the solution:

• Molarity (M) = Moles of solute / Volume of solution in liters
• Molarity = 6.67 moles / 1 L = 6.67 M

Thus, the molarity of the 50.00 weight% H2SO4 solution is approximately 6.67 M.

Finding Volume of Acid for 0.2 M Solution

Now, let’s determine the volume of the concentrated H2SO4 solution needed to prepare 1 liter of a 0.2 M H2SO4 solution.

Step 1: Use Molarity Equation

We can use the dilution equation, which states:

• C1V1 = C2V2

Where:

• C1 = concentration of the stock solution (6.67 M)
• V1 = volume of the stock solution needed (what we want to find)
• C2 = concentration of the diluted solution (0.2 M)
• V2 = volume of the diluted solution (1 L)

Step 2: Rearranging the Equation

Rearranging the equation to solve for V1 gives us:

• V1 = (C2 × V2) / C1

Step 3: Plugging in the Values

Now, substituting the known values:

• V1 = (0.2 M × 1 L) / 6.67 M ≈ 0.03 L

This means that you need approximately 0.03 L, or 30 mL, of the concentrated H2SO4 solution to prepare 1 liter of a 0.2 M solution.

In summary, the molarity of the 50.00 weight% H2SO4 solution is about 6.67 M, and to prepare a 0.2 M solution, you would need approximately 30 mL of the concentrated acid. Always remember to handle acids with care and follow proper safety protocols when performing such dilutions.