Problem 38 - Chemistry The Central Science In Si Units

Question

Sulfur is present in seawater to the extent of \(0.09 \%\) by mass. Assuming that the sulfur is present as sulfate, \(\mathrm{SO}_{4}^{2-}\), calculate the corresponding molar concentration of \(\mathrm{SO}_{4}^{2-}\) in seawater.

Step-by-Step Solution

Answer

The molar concentration of \( \mathrm{SO}_{4}^{2-} \) in seawater is approximately \( 0.0028 \text{ moles/L} \).

Step 1: Understand the Problem

We need to find the molar concentration of sulfate ions \( \mathrm{SO}_{4}^{2-} \) in seawater given that sulfur is present at \( 0.09\% \) by mass.

Step 2: Calculate Mass of Sulfate

Assume 1000 g of seawater to simplify calculations. The mass of sulfur present is \( 0.09\% \), which is 0.09 g of sulfur. Since sulfate is \( \mathrm{SO}_{4}^{2-} \), each mole of sulfate contains one mole of sulfur.

Step 3: Calculate Moles of Sulfur

Using the atomic mass of sulfur (32.07 g/mol), calculate moles of sulfur: \[ \text{Moles of } \mathrm{S} = \frac{0.09 \text{ g}}{32.07 \text{ g/mol}} \approx 0.0028 \text{ moles} \]

Step 4: Convert Moles of Sulfur to Moles of Sulfate

Since each mole of sulfate contains one mole of sulfur, there are also approximately \( 0.0028 \text{ moles} \) of \( \mathrm{SO}_{4}^{2-} \) in 1000 g of seawater.

Step 5: Calculate Molar Concentration

Assuming seawater density is approximately \( 1 \text{ g/mL} \), 1000 g of seawater corresponds to 1 L. The molarity of \( \mathrm{SO}_{4}^{2-} \) is therefore \[ \text{Molarity of } \mathrm{SO}_{4}^{2-} = 0.0028 \text{ moles/L} \]

Key Concepts

Sulfur Content in Seawater

In oceanic wonders, sulfur is naturally dissolved, predominantly in the form of sulfate ions, B2-\(\mathrm{SO}_4^{2-}\). Seawater contains an assortment of dissolved minerals, and sulfur contributes about \(0.09\%\) by mass. This means in every 1000 grams of seawater, there are about 0.09 grams of sulfur. To put this in perspective, the sulfur content is a small yet significant portion of the vast oceans, contributing to various biological and chemical processes.
The presence of sulfur as sulfate is vital for marine life, as it plays a crucial role in the sulfur cycle and supports the growth of plankton and other marine organisms. Understanding how sulfur exists in seawater is essential for marine biologists and chemists, as it impacts biodiversity, nutrient availability, and even ocean acidity levels.

Molarity Calculation

Calculating the molarity of any substance involves determining the number of moles of solute per liter of solution. Here, we need to find the molar concentration of sulfate ions, \(\mathrm{SO}_4^{2-}\), starting from a known mass percentage of sulfur in seawater.
First, assume 1000 g (1 kg) of seawater, containing \(0.09\%\) sulfur by mass, equaling 0.09 g sulfur. Convert this mass to moles using sulfur's atomic mass (32.07 g/mol): \[\text{Moles of Sulfur} = \frac{0.09\text{ g}}{32.07\text{ g/mol}} \approx 0.0028,\text{ moles}\]
Since each mole of sulfate contains one mole of sulfur, the moles of sulfate ions are similarly \(0.0028\) in a liter of seawater (assuming the density is \(1\, \text{g/mL}\)). Therefore, the molarity of \(\mathrm{SO}_4^{2-}\) is \(0.0028\, \text{mol/L}\).
This process highlights the relationship between mass percentage and molarity, a fundamental concept in chemistry which allows us to translate solid weights into useful liquid concentrations.

Sulfate Ions in Chemistry

Sulfate ions, \(\mathrm{SO}_4^{2-}\), are essential in chemistry for their involvement in numerous reactions and industrial processes. Composed of one sulfur atom bonded to four oxygen atoms, these ions bear a double negative charge, making them reactive and able to form various compounds.
In the context of seawater, sulfate ions are a key component. Not only do they contribute to water's mineral content, but they also interact with other elements and compounds, influencing water chemistry. Understanding sulfate ions is crucial for fields such as environmental science and geochemistry, as they play a role in processes like the weathering of rocks, influencing soil and water composition, and even in industrial applications like mining and wastewater treatment.
Whether examining their impact on ecosystems or leveraging their properties for industrial use, sulfate ions remain a fundamental topic within chemical studies.