A solution of palmitic acid in benzene contains 4.24g of acid per litre. When this solution is dropped on a surface, benzene gets evaporated and palmitic acid forms a unimolecular film on the surface. If we wish to cover an area of 500 cm² with unimolecular film, what volume of solution should be used? The area covered by one palmitic acid molecule may be taken as 0.21 nm².

Mol. Weight of palmitic acid= 256

To determine the volume of the palmitic acid solution needed to cover an area of 500 cm² with a unimolecular film, we can break down the problem into a series of logical steps. First, we need to calculate the number of palmitic acid molecules required to cover the specified area, and then we can find out how much of the solution is necessary to obtain that number of molecules.

Step 1: Calculate the Total Number of Molecules Required

We know that the area covered by one molecule of palmitic acid is 0.21 nm². To find out how many molecules are needed to cover 500 cm², we first need to convert the area from cm² to nm².

• 1 cm = 10⁷ nm
• 1 cm² = (10⁷ nm)² = 10¹⁴ nm²

Now, converting 500 cm² to nm²:

500 cm² = 500 × 10¹⁴ nm² = 5 × 10¹⁶ nm²

Next, we can find the number of molecules required:

Number of molecules = Total area / Area per molecule = (5 × 10¹⁶ nm²) / (0.21 nm²) ≈ 2.38 × 10¹⁷ molecules

Step 2: Calculate the Moles of Palmitic Acid Needed

To find out how many moles of palmitic acid correspond to the number of molecules calculated, we use Avogadro's number, which is approximately 6.022 × 10²³ molecules/mol.

Moles of palmitic acid = Number of molecules / Avogadro's number = (2.38 × 10¹⁷) / (6.022 × 10²³) ≈ 3.95 × 10^-7 moles

Step 3: Calculate the Mass of Palmitic Acid Required

Using the molar mass of palmitic acid (256 g/mol), we can find the mass needed:

Mass = Moles × Molar mass = (3.95 × 10^-7 moles) × (256 g/mol) ≈ 1.01 × 10^-4 g

Step 4: Determine the Volume of Solution Needed

Now, we know that the solution contains 4.24 g of palmitic acid per liter. To find the volume of the solution that contains the required mass of palmitic acid, we can use the following formula:

Volume = Mass / Concentration

Substituting the values:

Volume = (1.01 × 10^-4 g) / (4.24 g/L) ≈ 2.38 × 10^-5 L

To convert this volume into milliliters (since 1 L = 1000 mL):

Volume ≈ 2.38 × 10^-5 L × 1000 mL/L ≈ 0.0238 mL

Final Result

To cover an area of 500 cm² with a unimolecular film of palmitic acid, you would need approximately 0.0238 mL of the solution. This calculation illustrates how we can use molecular dimensions and concentrations to solve practical problems in chemistry.