You collected a water sample from your shower containing (3.2 mM Ca2+)+(1.1 Mm Mg2+). Express the hardness of water in terms of mg CaCO3/L. (FM for CaCO3+100.09) I have no idea how to do this problem. Can anyone show me a step by step on how to work through it?
assuming your sample was 1L,
3.2mM Ca implies 3.2mmoles of CaCO3.
So, that's .0032*100.09 = 0.32g/L
I believe the hardness is the sum of the Ca and Mg ions.
To calculate the hardness of water in terms of mg CaCO3/L, we need to determine the concentration of calcium carbonate that is equivalent to the calcium and magnesium ions present in the water sample.
Step 1: Calculate the molar mass of CaCO3:
The formula mass (FM) for CaCO3 is given as 100.09 g/mol.
Step 2: Calculate the concentration of Ca2+ and Mg2+ ions in mol/L:
Given that the concentration of Ca2+ ions is 3.2 mM (millimolar = 10^-3 mol/L) and the concentration of Mg2+ ions is 1.1 Mm (micromolar = 10^-6 mol/L), we convert them to mol/L:
3.2 mM = 3.2 × 10^-3 mol/L
1.1 Mm = 1.1 × 10^-6 mol/L
Step 3: Calculate the molar mass of Ca2+ and Mg2+ ions:
The molar mass of Ca2+ is 40.08 g/mol, and the molar mass of Mg2+ is 24.31 g/mol.
Step 4: Convert the molar quantities of Ca2+ and Mg2+ to mass quantities of CaCO3:
To do this, we need to determine the equivalent molar ratio of Ca2+ or Mg2+ to CaCO3. Since CaCO3 has one Ca2+ ion per molecule, the molar ratio is 1:1.
For Ca2+ ions:
mass of CaCO3 = (concentration of Ca2+ in mol/L) × (molar mass of Ca2+) / (molar mass of CaCO3)
= (3.2 × 10^-3 mol/L) × (40.08 g/mol) / (100.09 g/mol)
= 1.282 × 10^-3 g/L
For Mg2+ ions:
mass of CaCO3 = (concentration of Mg2+ in mol/L) × (molar mass of Mg2+) / (molar mass of CaCO3)
= (1.1 × 10^-6 mol/L) × (24.31 g/mol) / (100.09 g/mol)
= 2.656 × 10^-9 g/L
Step 5: Calculate the total hardness of the water sample:
Total hardness = mass of CaCO3 from Ca2+ ions + mass of CaCO3 from Mg2+ ions
= 1.282 × 10^-3 g/L + 2.656 × 10^-9 g/L
= 1.282 × 10^-3 g/L
Therefore, the hardness of the water sample in terms of mg CaCO3/L is approximately 1.282 mg CaCO3/L.
To calculate the hardness of water in terms of mg CaCO3/L, you need to determine the total concentration of calcium and magnesium ions and convert it into an equivalent concentration of CaCO3.
Here are the step-by-step instructions to solve this problem:
Step 1: Calculate the concentration of calcium ions (Ca2+) and magnesium ions (Mg2+) separately.
In this case, the concentration of Ca2+ is given as 3.2 mM (millimoles per liter) and the concentration of Mg2+ is given as 1.1 Mm (micromoles per liter).
Step 2: Calculate the molar mass of CaCO3.
The formula weight for CaCO3 is given as 100.09 g/mol (grams per mole).
Step 3: Convert the concentration of calcium ions (Ca2+) from millimoles to moles.
Since 1 mM = 0.001 mol/L, you can convert the concentration of Ca2+ from millimoles to moles by multiplying it by 0.001.
Ca2+ concentration in moles = 3.2 mM × 0.001 mol/mM = 0.0032 mol/L
Step 4: Convert the concentration of calcium ions (Ca2+) from moles to grams.
To convert the concentration from moles to grams, multiply it by the molar mass of calcium (Ca2+).
Ca2+ mass in grams = Ca2+ concentration in moles × molar mass of Ca2+
Ca2+ mass in grams = 0.0032 mol/L × 40.08 g/mol (molar mass of Ca2+) = 0.128 g/L
Step 5: Convert the concentration of magnesium ions (Mg2+) from micromoles to moles.
Since 1 Mm = 0.000001 mol/L, you can convert the concentration of Mg2+ from micromoles to moles by multiplying it by 0.000001.
Mg2+ concentration in moles = 1.1 Mm × 0.000001 mol/Mm = 0.0000011 mol/L
Step 6: Convert the concentration of magnesium ions (Mg2+) from moles to grams.
To convert the concentration from moles to grams, multiply it by the molar mass of magnesium (Mg2+).
Mg2+ mass in grams = Mg2+ concentration in moles × molar mass of Mg2+
Mg2+ mass in grams = 0.0000011 mol/L × 24.31 g/mol (molar mass of Mg2+) = 0.000026841 g/L
Step 7: Calculate the total mass of CaCO3.
The total mass of CaCO3 is calculated by adding the mass of calcium (Ca2+) and the mass of magnesium (Mg2+).
Total mass of CaCO3 in grams = Ca2+ mass in grams + Mg2+ mass in grams
Total mass of CaCO3 in grams = 0.128 g/L + 0.000026841 g/L = 0.128026841 g/L
Step 8: Convert the total mass of CaCO3 from grams to milligrams.
To convert the total mass from grams to milligrams, multiply it by 1000.
Total mass of CaCO3 in milligrams = Total mass of CaCO3 in grams × 1000
Total mass of CaCO3 in milligrams = 0.128026841 g/L × 1000 = 128.026841 mg/L
So, the hardness of water in terms of mg CaCO3/L is approximately 128.03 mg/L.