Problem 120 - Chemistry The Science in Context

Question

A 1 -liter sample of seawater contains \(19.4 \mathrm{g}\) of \(\mathrm{Cl}^{-}, 10.8 \mathrm{g}\) of \(\mathrm{Na}^{+},\) and \(1.29 \mathrm{g}\) of \(\mathrm{Mg}^{2+}\) a. How many moles of each ion are present? b. If we evaporated the seawater, would there be enough Cl "present to form the chloride salts of all the sodium and magnesium present?

Step-by-Step Solution

Answer

Answer: No, there is not enough Cl- present to form chloride salts with all the sodium and magnesium ions in the 1-liter seawater sample.

Step 1: Calculate moles of ions

To calculate the number of moles of each ion, we'll use the formula number of moles = (mass)/(molar mass) The molar mass of Cl- is 35.45 g/mol The molar mass of Na+ is 22.99 g/mol The molar mass of Mg2+ is 24.31 g/mol Now we can calculate the moles for each ion. Moles of Cl- = (19.4 g)/(35.45 g/mol) = 0.547 moles Moles of Na+ = (10.8 g)/(22.99 g/mol) = 0.470 moles Moles of Mg2+ = (1.29 g)/(24.31 g/mol) = 0.0530 moles

Step 2: Determine if there is enough Cl- to form chloride salts

The next step is to evaluate if the moles of Cl- are sufficient to form the corresponding salts with Na+ and Mg2+. The ionic salts we can form are NaCl and MgCl2. For each mole of Na+, one mole of Cl- is needed to form NaCl. For each mole of Mg2+, two moles of Cl- are needed to form MgCl2. We'll calculate the total moles of Cl- needed to form the salts: Total moles of Cl- needed = (0.470 moles of Na+ x 1 Cl-) + (0.0530 moles of Mg2+ x 2 Cl-) Total moles of Cl- needed = 0.470 + 0.106 = 0.576 moles Now let's compare the moles of Cl- needed with the moles of Cl- present in the seawater sample. The seawater contains 0.547 moles of Cl- and we need 0.576 moles of Cl- to form the corresponding salts.

Step 3: Conclusion

As the moles of Cl- (0.547) in the seawater are less than the required moles of Cl- (0.576) to form salts with all the sodium and magnesium present, there is not enough Cl- present to form the chloride salts of all the sodium and magnesium ions in the 1-liter seawater sample.

Key Concepts

Molar Mass

Molar mass is an essential concept in chemistry, especially when it comes to calculating the amount of substances. It is defined as the mass of one mole of a chemical element or compound and is expressed in grams per mole (g/mol). Each element has its own molar mass, which is typically found on the periodic table. For example, the molar mass of chlorine (\(\text{Cl}^{-}\)) is 35.45 g/mol, the molar mass of sodium (\(\text{Na}^{+}\)) is 22.99 g/mol, and magnesium (\(\text{Mg}^{2+}\)) has a molar mass of 24.31 g/mol.

• To calculate the number of moles of a substance, you need to divide the mass of the substance by its molar mass.
• For example, if you have 19.4 g of \(\text{Cl}^{-}\), you can calculate the moles by dividing 19.4 by 35.45, resulting in approximately 0.547 moles.

Being comfortable with molar mass calculations is critical for understanding more complex chemical equations and reactions. It allows you to convert between the mass of a substance and the number of particles or moles, which is fundamental for stoichiometry.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relationships between the relative quantities of reactants and products in chemical reactions. It is based on the conservation of mass where the number of atoms of each element is balanced on both sides of the chemical equation.
When determining if there are sufficient amounts of reactants to make products, stoichiometry plays a key role:

• For forming NaCl from Na and Cl, the reaction uses a 1:1 mole ratio. This means each mole of \(\text{Na}^{+}\) will react with one mole of \(\text{Cl}^{-}\).
• In forming MgCl2, the ratio changes to 1:2, where each mole of \(\text{Mg}^{2+}\) requires two moles of \(\text{Cl}^{-}\).

In the given scenario, you calculate the total external chloride ions required:

• Multiply the amount of \(\text{Na}^{+}\) moles (0.470) by 1, and
• multiply the amount of \(\text{Mg}^{2+}\) moles (0.053) by 2.
• Add these two results to find the total moles of Cl needed.

Understanding stoichiometry allows chemists to predict how much of each reactant is necessary to produce a desired amount of product and vice versa.

Seawater Chemistry

Seawater chemistry involves studying the multitude of substances dissolved in seawater. It is a complex chemical solution, containing a wide range of dissolved salts, gases, and even nutrients. The most abundant ions found in seawater are chloride (\(\text{Cl}^{-}\)), sodium (\(\text{Na}^{+}\)), and magnesium (\(\text{Mg}^{2+}\)). These ions contribute significantly to the salinity of seawater.
The interaction of ions is a critical component of seawater chemistry:

• Chloride ions are the most prevalent ions dissolved in seawater, and they play an essential role in marine chemical reactions.
• Sodium ions are responsible for the classic salty taste of seawater.
• Magnesium ions, besides contributing to salinity, also have roles in marine biology and geochemical cycles.

In practical scenarios, such as attempting to remove salts through evaporation, the interaction between these ions determines what compounds are formed. Even in a simple act of evaporating seawater, the existing chemical makeup significantly influences which salts can be isolated or crystallized from the solution. This is especially important for industries, such as desalination or salt production, where understanding these principles helps ensure effective and efficient processing.