Problem 105 - Chemistry: An Atoms-Focused Approach

Question

The average concentration of sulfate in surface seawater is about \(0.028 M .\) The average concentration of \(\mathrm{Sr}^{2+}\) is \(9 \times 10^{-5} M .\) Is the concentration of strontium in the sea significantly controlled by the insolubility of its sulfate salt?

Step-by-Step Solution

Answer

Answer: No, the concentration of strontium in seawater is not significantly controlled by the insolubility of its sulfate salt. The observed concentration of strontium ions in seawater is higher than what would be expected from the solubility equilibrium of strontium sulfate.

Step 1: Find the solubility product constant (Ksp) for strontium sulfate

First, we need to find the solubility product constant (Ksp) for strontium sulfate (SrSO₄). You can find this value in a chemistry reference table or textbook. In this case, the Ksp for strontium sulfate is \(2.8 \times 10^{-7}\).

Step 2: Calculate the ionic product (Q) for the given concentrations

The ionic product of strontium sulfate is found using the formula \(Q = [Sr^{2+}][SO₄^{2-}]\). We are given the average concentration of sulfate ions (\(0.028 M\)) and strontium ions (\(9 \times 10^{-5} M\)) in seawater. Now, let's calculate the ionic product: \(Q = (0.028)(9 \times 10^{-5}) = 2.52 \times 10^{-6}\).

Step 3: Compare the ionic product (Q) with the solubility product constant (Ksp)

To determine whether the strontium concentration in the sea is significantly controlled by the insolubility of its sulfate salt, we need to compare the calculated ionic product (Q) with the solubility product constant (Ksp) of strontium sulfate (SrSO₄). We found earlier that Ksp = \(2.8 \times 10^{-7}\) and Q = \(2.52 \times 10^{-6}\). Since Q > Ksp, this indicates that the concentration of strontium ions in the seawater is higher than what is expected from the solubility equilibrium of strontium sulfate.

Step 4: Conclusion

The concentration of strontium in the sea is not significantly controlled by the insolubility of its sulfate salt. The observed concentration of strontium ions in seawater is higher than what would be expected from the solubility equilibrium of strontium sulfate.

Key Concepts

Ionic Product

The concept of the ionic product is crucial in determining the solubility behavior of salts in solution. It is represented by the symbol \(Q\) and is calculated in a solution by multiplying the molar concentrations of the ions present. For strontium sulfate in seawater, the ionic product \(Q\) is calculated using the formula:

• \(Q = [\text{Sr}^{2+}][\text{SO}_4^{2-}]\)

Given that the concentration of sulfate is \(0.028 \ M\) and that of strontium ions is \(9 \times 10^{-5} \ M\), the ionic product becomes:

• \(Q = (0.028)(9 \times 10^{-5}) = 2.52 \times 10^{-6}\)

This value is used to ultimately understand if the mineral is at equilibrium, precipitating, or dissolving further into the solution.

Comparing \(Q\) with the solubility product constant \(K_{sp}\) can indicate whether the salt will remain dissolved or begin to precipitate.

Strontium Sulfate

Strontium sulfate, denoted chemically as \(\text{SrSO}_4\), is a slightly soluble salt found in seawater and known for its low solubility product constant \(K_{sp}\). At equilibrium, where no more undissolved salt will enter the solution, its \(K_{sp}\) is calculated to be \(2.8 \times 10^{-7}\).

The balance between dissolved ions and solid salt is determined by comparing the ionic product \(Q\) to \(K_{sp}\):

• If \(Q < K_{sp}\), the solution can dissolve more strontium sulfate.
• If \(Q = K_{sp}\), the solution is at equilibrium, with no net change.
• When \(Q > K_{sp}\), the solution is supersaturated, leading to precipitation.

In the seawater exercise, the calculated \(Q\) was greater than the \(K_{sp}\), indicating that the solution is supersaturated, suggesting that some strontium ions could precipitate out in the form of strontium sulfate.

Seawater Chemistry

Seawater chemistry provides a fascinating and complex system where multiple ions coexist in dynamic balance. Within this context, understanding the concentrations of various ions like \(\text{Sr}^{2+}\) and \(\text{SO}_4^{2-}\) is essential.

The concentration of specific ions in seawater, such as strontium, depends on several factors, including input from rivers, atmospheric deposition, and biological cycling. Strontium's presence in seawater averages around \(9 \times 10^{-5} \ M\), and sulfate is present at \(0.028 \ M\).

• Seawater is usually a dilute mixture and despite its complex composition, it maintains a rather stable ionic strength.
• The high ionic strength can affect solubility, where salts like strontium sulfate may behave differently compared to less ionic environments.
• In the seawater scenario, with \(Q > K_{sp}\), strontium's higher concentration indicates it's not significantly controlled by its sulfate salt's insolubility, likely due to overlapping influences of other seawater chemistry processes.

This insight shows how the interaction of multiple elements in seawater can lead to chemistry outcomes that differ from simplistic models based solely on solubility.