Question

The hardness of water sample ( in terms of equivalents of $CaCO{}_3$) containing $10{}^{ - 3}$M $CaSO{}_4$ is; ( molar mass of $CaSO{}_4 = 136$g/mol)

Answer 1

Hardness of water is the water with high amount or the water which is rich in mineral content this kind of water is known as hard water. Let us first find the amount of sulphate in water and then the hardness of calcium carbonate.

Complete step by step solution:
The concentration of $CaSO{}_4$ in water is given:
The molarity of $CaSO{}_4$ is $10{}^{ - 3}$ that means in $1000$ ml of water there is presence of $10{}^{ - 3}$ moles of $CaSO{}_4$.
Now we know the number of moles in $1000$ml of $CaSO{}_4$, with the help of this and the molar mass we can now find out the weight of $CaSO{}_4$ in water.
Therefore,
Weight of CaSO{}_4$$$$ = 10{}^{ - 3} \times 136g $= 0.136$g
Hence there is $0.136$gram of $CaSO{}_4$in one litre of water.
Now we will compare this in terms of $CaCO{}_3$to find the hardness.
The molecular weight of $CaSO{}_4$is $136$g and of $CaCO{}_3$ is $100$g
$0.136g$of CaSO{}_4$$$$ \to \dfrac{{100}}{{136}} \times 0.136
=$10{}^{ - 1}$or $0.1$gram of $CaCO{}_3$
Now let us find the hardness of $CaCO{}_3$

Therefore, hardness = $\dfrac{{WCaSO{}_4}}{{WH{}_2O}} \times 10{}^6$
As we are finding the answer in ppm we multiply it with $10{}^6$
$= \dfrac{{0.1}}{{1000}} \times 10{}^6 \\\ = 0.1 \times 10{}^3 \\\ = 10{}^2 \\\ = 100 \\\$
The hardness of the water sample is $100$ppm .

Additional Information:
Hard water is basically water with a high amount of mineral content. This forms when water percolates through the deposits of chalk, limestone etc which is made mostly of iron, sulphates, carbonates, and bicarbonates. Iron oxides give reddish brown colouration to hard water deposits. Hard water has few health benefits.

Note: molarity also known as molar concentration is a measure of a solute in solution in terms of amount of the given substance per unit volume of solution. The most common unit of molarity is moles per litre.