A hardwater sample contains 68g of CaSO4 in 10litre. Calculate the hardness.
Hardness is usually calculated at mg/L CaCO3. First convert 68 g CaSO4 to CaCO3.
68 g CaSO4 x (molar mass CaCO3/molar mass CaSO4) = ?
Then convert g CaCO3 to mg.
Finally, mg CaCO3/10 L = ? mg/L
To calculate the hardness of the water sample, you need to understand the concept of hardness in water and the role of calcium sulfate (CaSO4) in determining it.
Hardness in water refers to the presence of dissolved minerals, primarily calcium (Ca) and magnesium (Mg) ions. These minerals can be present in various forms, such as calcium carbonate (CaCO3) or calcium sulfate (CaSO4). The quantity of these minerals determines the degree of water hardness.
In this case, the water sample contains 68g of calcium sulfate (CaSO4) in a volume of 10 liters. To calculate the hardness, follow these steps:
Step 1: Calculate the molar mass of calcium sulfate (CaSO4).
The molar mass of calcium (Ca) is 40.08 g/mol.
The molar mass of sulfur (S) is 32.07 g/mol.
The molar mass of oxygen (O) is 16.00 g/mol.
So, the molar mass of calcium sulfate (CaSO4) can be calculated as:
(1 * Ca) + (1 * S) + (4 * O)
= 40.08 g/mol + 32.07 g/mol + (4 * 16.00 g/mol)
= 136.14 g/mol
Step 2: Calculate the number of moles of calcium sulfate (CaSO4) in the water sample.
To calculate the number of moles, divide the mass of calcium sulfate by its molar mass.
Number of moles = Mass / Molar mass
= 68 g / 136.14 g/mol
= 0.5 mol
Step 3: Calculate the concentration of calcium sulfate (CaSO4) in the water sample.
Concentration = Number of moles / Volume
= 0.5 mol / 10 L
= 0.05 mol/L
Step 4: Calculate the hardness.
Hardness is typically expressed in milligrams per liter (mg/L) or parts per million (ppm). Since the concentration was calculated in moles per liter (mol/L), you need to convert it to mg/L.
To perform this conversion, multiply the concentration by the molar mass of calcium (Ca), as calcium ions are responsible for the hardness.
Hardness (mg/L) = Concentration (mol/L) * Molar mass of calcium (Ca)
= 0.05 mol/L * 40.08 g/mol
= 2.004 mg/L or 2.004 ppm
Therefore, the hardness of the hard water sample containing 68g of calcium sulfate (CaSO4) in 10 liters is 2.004 mg/L or 2.004 ppm.