Question(c) In water treatment plant, calcium sulphate, $\mathrm{CaSO}_{4}$ is often formed as a precipitate which can clog pipes and reduce the efficiency of the system. The solubility product constant for calcium sulphate, $\mathrm{CaSO}_{4}$ is $2.4 \times 10^{-5}$ at room temperature. The plant has a solution containing 0.01 M of calcium ions, $\mathrm{Ca}^{2+}$ . If the concentration of sulphate ion, $\mathrm{SO}_{4}{ }^{2-}$ in the water is initially $1.5 \times 10^{-3} \mathrm{M}$ , will a precipitate of calcium sulphate form? [3 marks]

Studdy Solution

STEP 1

1. The solubility product constant ( $K_{sp}$ ) for calcium sulfate ( $\text{CaSO}_4$ ) is $2.4 \times 10^{-5}$ .
2. The concentration of calcium ions ( $\text{Ca}^{2+}$ ) is $0.01 \, \text{M}$ .
3. The initial concentration of sulfate ions ( $\text{SO}_4^{2-}$ ) is $1.5 \times 10^{-3} \, \text{M}$ .
4. A precipitate will form if the ionic product exceeds the solubility product constant.

STEP 2

1. Calculate the ionic product of the solution.
2. Compare the ionic product with the solubility product constant.
3. Determine if a precipitate will form.

STEP 3

Calculate the ionic product ( $Q$ ) of the solution using the concentrations of calcium ions and sulfate ions:
$Q = [\text{Ca}^{2+}][\text{SO}_4^{2-}] = (0.01)(1.5 \times 10^{-3})$
$Q = 1.5 \times 10^{-5}$

STEP 4

Compare the calculated ionic product ( $Q = 1.5 \times 10^{-5}$ ) with the solubility product constant ( $K_{sp} = 2.4 \times 10^{-5}$ ).

STEP 5

Since $Q < K_{sp}$ , the solution is unsaturated with respect to calcium sulfate, and no precipitate will form.
Conclusion: A precipitate of calcium sulfate will not form under the given conditions.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms