Calculation of Total Hardness:

To calculate the total hardness of the water sample, we need to convert the concentrations of CaCl2 and MgCl2 to an equivalent concentration of calcium carbonate (CaCO3). This is because the hardness of water is commonly expressed in terms of the concentration of CaCO3.

The molar mass of CaCl2 is 110.98 g/mol and the molar mass of MgCl2 is 95.21 g/mol. We can use these values to convert the concentrations of CaCl2 and MgCl2 to moles.

Converting CaCl2 to Moles:
Given: 5.56 mg of CaCl2
Molar mass of CaCl2 = 110.98 g/mol

Converting mg to g:
5.56 mg = 5.56 × 10^(-3) g

Converting g to moles:
Moles of CaCl2 = (5.56 × 10^(-3) g) / (110.98 g/mol)

Converting MgCl2 to Moles:
Given: 4.47 mg of MgCl2
Molar mass of MgCl2 = 95.21 g/mol

Converting mg to g:
4.47 mg = 4.47 × 10^(-3) g

Converting g to moles:
Moles of MgCl2 = (4.47 × 10^(-3) g) / (95.21 g/mol)

Calculating Total Moles of CaCO3:
Since 1 mole of CaCl2 produces 1 mole of CaCO3 and 1 mole of MgCl2 produces 1 mole of CaCO3, the total moles of CaCO3 can be calculated by adding the moles of CaCl2 and MgCl2.

Total moles of CaCO3 = Moles of CaCl2 + Moles of MgCl2

Converting Total Moles to ppm:
To convert the total moles of CaCO3 to ppm, we need to multiply by the molar mass of CaCO3 and divide by the volume of the water sample.

Total ppm of CaCO3 = (Total moles of CaCO3 * Molar mass of CaCO3) / Volume of water sample

Plugging in the Values:
Given: Volume of water sample = 1 liter

Total moles of CaCO3 = (Moles of CaCl2 + Moles of MgCl2)
Molar mass of CaCO3 = 100.09 g/mol (molar mass of calcium) + 2*(16.00 g/mol) (molar mass of oxygen)

Total ppm of CaCO3 = ((Moles of CaCl2 + Moles of MgCl2) * Molar mass of CaCO3) / Volume of water sample

Simplifying the Equation:
Total ppm of CaCO3 = ((Moles of CaCl2 + Moles of MgCl2) * (100.09 g/mol + 2*(16.00 g/mol))) / 1 liter

Calculating the Total ppm:
Now, we can substitute the values of moles of CaCl2 and Moles of MgCl2 into the equation and calculate the total