What is the percent mass of calcium in a calcium supplement if 1.28-g of calcium carbonate is extracted from a 2.72-g pill?
To calculate the percent mass of calcium in a calcium supplement, we need to determine the mass of calcium in the calcium carbonate and then find the percentage of that mass with respect to the total mass of the pill.
Here are the steps to solve the problem:
Step 1: Determine the molar mass of calcium carbonate (CaCO3).
The molar mass of calcium carbonate is calculated by adding up the atomic masses of its constituent elements:
Ca: 40.08 g/mol
C: 12.01 g/mol
O: 16.00 g/mol (there are three oxygen atoms in calcium carbonate)
Molar mass of CaCO3 = (1 × 40.08 g/mol) + (1 × 12.01 g/mol) + (3 × 16.00 g/mol) = 100.09 g/mol
Step 2: Calculate the number of moles of calcium carbonate.
To find the number of moles, divide the given mass (1.28 g) by the molar mass of calcium carbonate (100.09 g/mol):
Moles of CaCO3 = 1.28 g / 100.09 g/mol = 0.01279 mol (rounded to five decimal places)
Step 3: Determine the molar mass of calcium.
Since 1 mole of calcium carbonate (CaCO3) contains 1 mole of calcium (Ca), the molar mass of calcium is the same as the atomic mass of calcium, which is 40.08 g/mol.
Step 4: Calculate the mass of calcium in the calcium carbonate.
Multiply the number of moles of calcium carbonate (0.01279 mol) by the molar mass of calcium (40.08 g/mol):
Mass of calcium = 0.01279 mol × 40.08 g/mol = 0.5132 g (rounded to four decimal places)
Step 5: Calculate the percent mass of calcium.
To get the percent mass, divide the mass of calcium (0.5132 g) by the mass of the pill (2.72 g) and multiply by 100%:
Percent mass of calcium = (0.5132 g / 2.72 g) × 100% ≈ 18.88%
Therefore, the percent mass of calcium in the calcium supplement is approximately 18.88%.
Ca comprises 2/3 of the 1.28g CaCO3, or 0.853g
So, assuming that all of the calcium is contained in the CaCO3, the 0.853g is 31.37% of the 2.72g pill