The hardness of a water sample (in terms of equivalents of CaCO3) containing 10⁻⁷ M CaSO4 is: [Molar mass of CaSO4 = 136 g mol⁻¹]

The hardness of water is usually expressed in terms of ppm (parts per million) of CaCO3. We are given that the concentration of CaSO4 is 10⁻⁷ M.

1. Moles of CaSO4:
   We have 10⁻⁷ moles of CaSO4 per liter of water.

2. Moles of Ca²⁺:
   Since CaSO4 dissociates completely into one Ca²⁺ ion and one SO₄²⁻ ion, we also have 10⁻⁷ moles of Ca²⁺ ions per liter.

3. Equivalents of Ca²⁺:
   The charge of Ca²⁺ is +2, so there are 2 equivalents of Ca²⁺ per mole of Ca²⁺. Therefore, we have 2 * 10⁻⁷ equivalents of Ca²⁺ per liter.

4. Equivalents of CaCO3:
   The hardness is expressed in terms of CaCO3, which also has a +2 charge for Ca²⁺. Thus, the number of equivalents of CaCO3 is equal to the number of equivalents of Ca²⁺, which is 2 * 10⁻⁷ equivalents per liter.

5. Mass of CaCO3:
   The molar mass of CaCO3 is approximately 100 g/mol. Therefore, the mass of CaCO3 equivalent to 2 * 10⁻⁷ equivalents is:
   (2 * 10⁻⁷ equivalents) * (100 g/mol) / (2 equivalents/mol) = 10⁻⁵ g of CaCO3 per liter.

6. Concentration in ppm:
   To express this concentration in ppm (parts per million), we use the following conversion:
   1 ppm = 1 mg/L
   10⁻⁵ g = 10⁻² mg
   Therefore, the hardness of the water sample is 10⁻² mg/L, which is 10 ppm.

Therefore, the hardness of the water sample is 10 ppm.