Calculate the number of phosphorus atoms in 17.0g sample of calcium phosphate
To calculate the number of phosphorus atoms in a sample of calcium phosphate, you need to follow several steps. Here's the step-by-step process:
1. Determine the molar mass of calcium phosphate (Ca3(PO4)2):
- The molar mass of calcium (Ca) is 40.08 g/mol.
- The molar mass of phosphorus (P) is 30.97 g/mol.
- The molar mass of oxygen (O) is 16.00 g/mol.
- Since there are three calcium atoms (Ca) and two phosphate groups (PO4) in calcium phosphate, the molar mass can be calculated as follows:
Molar mass of calcium phosphate = (3 * molar mass of calcium) + (2 * (molar mass of phosphorus + 4 * molar mass of oxygen))
2. Calculate the number of moles of calcium phosphate:
- Convert the given mass of the sample into moles using the molar mass of calcium phosphate:
Moles of calcium phosphate = Mass of sample / Molar mass of calcium phosphate
3. Determine the number of moles of phosphorus:
- Since there are two moles of phosphorus per mole of calcium phosphate, multiply the number of moles of calcium phosphate by two:
Moles of phosphorus = 2 * Moles of calcium phosphate
4. Calculate the Avogadro's number (6.022 x 10^23) to determine the number of phosphorus atoms:
- Multiply the number of moles of phosphorus by Avogadro's number:
Number of phosphorus atoms = Moles of phosphorus * Avogadro's Number
Let's now perform the calculation:
1. Molar mass of calcium phosphate:
Molar mass of calcium phosphate = (3 * 40.08 g/mol) + (2 * (30.97 g/mol + 4 * 16.00 g/mol))
= 310.18 g/mol
2. Moles of calcium phosphate:
Moles of calcium phosphate = 17.0 g / 310.18 g/mol
≈ 0.0548 mol
3. Moles of phosphorus:
Moles of phosphorus = 2 * 0.0548 mol
≈ 0.1096 mol
4. Number of phosphorus atoms:
Number of phosphorus atoms = 0.1096 mol * (6.022 x 10^23 atoms/mol)
≈ 6.60 x 10^22 phosphorus atoms
Therefore, there are approximately 6.60 x 10^22 phosphorus atoms in a 17.0g sample of calcium phosphate.