how do I calculate the area occupied by one single molecule, given # of molecules per meter^2 (9.6e15), the Molarity? (.1 m/dm^3) and surface excess? (1.6e-8)
if it is one molecule thick, do the reciprocal of number of molecues/area.
area of one molecule=1/(molecules/area)
To calculate the area occupied by one single molecule, we need to use the following formula:
Area = Avogadro's number / (Molecules per meter^2 * Molarity * Surface excess)
Here's how to calculate it step by step:
Step 1: Convert the units of Molarity from m/dm^3 to molecules/m^2.
To do this, we need to multiply by Avogadro's number (6.022 × 10^23 molecules/mole):
Molecules per m^2 = Molarity * Avogadro's number
Molecules per m^2 = 0.1 m/dm^3 * (6.022 × 10^23 molecules/mole)
Step 2: Calculate the area by plugging the values into the formula.
Area = Avogadro's number / (Molecules per meter^2 * Molarity * Surface excess)
Area = (6.022 × 10^23) / (9.6 × 10^15 molecules per m^2 * 0.1 m/dm^3 * 1.6 × 10^-8)
Step 3: Simplify the expression.
Area = (6.022 × 10^23) / (1.536 × 10^8)
Area = 3.92 × 10^15 square meters
Therefore, the area occupied by one single molecule is approximately 3.92 × 10^15 square meters.
To calculate the area occupied by one single molecule, you'll need to use the given information and formulas related to molarity and surface excess.
1. Start by converting the molarity from units of m/dm^3 to molecules/meter^3.
- Since 1 m^3 = 1,000,000 dm^3, multiply the molarity (0.1 m/dm^3) by 1,000,000 to get the molarity in units of molecules/m^3.
2. Calculate the number of molecules in a single square meter (m^2) using the given number of molecules per meter^2 (9.6e15).
- Multiply the given number of molecules per meter^2 (9.6e15) by the molarity calculated in step 1. This will give you the number of molecules in one cubic meter (m^3).
3. Calculate the volume occupied by a single molecule in cubic meters (m^3).
- Divide the volume of the one cubic meter (m^3) by the number of molecules calculated in step 2. This will give you the volume occupied by one single molecule.
4. Convert the volume occupied by one molecule from cubic meters (m^3) to square meters (m^2).
- Since the volume is in cubic meters, convert it to square meters by taking the square root of the calculated volume.
5. Calculate the area occupied by one single molecule by using the formula for surface excess.
- Multiply the square root of the volume occupied by one molecule (found in step 4) by the surface excess (1.6e-8). This will give you the area occupied by one single molecule.
By following these steps, you can determine the area occupied by one single molecule using the given information of molarity, number of molecules per meter^2, and surface excess.