Question

Although there are many ions in seawater, the overall charges of the dissolved cations and anions must maintain charge neutrality. Consider only the six most abundant ions in seawater, as listed in Table \(18.5\left(\mathrm{Cl}^{-}, \mathrm{Na}^{+},\right.\) \(\mathrm{SO}_{4}^{2-}, \mathrm{Mg}^{2+}, \mathrm{Ca}^{2+},\) and \(\left.\mathrm{K}^{+}\right),\) calculate the total charge in Coulombs of the cations in \(1.0 \mathrm{~L}\) of seawater. Calculate the total charge in Coulombs of the anions in \(1.0 \mathrm{~L}\) of seawater. To how many significant figures are the two numbers equal?

Short answer

In summary, to calculate the total charge of cations and anions in 1.0 L of seawater, you need to follow these steps: 1. Determine the concentrations of the ions listed in Table 18.5 (Cl-, Na+, SO4(2-), Mg2+, Ca2+, and K+). 2. Calculate the moles of each ion in 1 L of seawater by multiplying their concentrations (in moles/L) by the volume of seawater (1 L). 3. Calculate the total charge of cations and anions by multiplying the number of moles of each ion by their respective charges (in elementary charge units, e) and the elementary charge (1.602×10^{-19} C). Sum up the charges separately for cations and anions. 4. Compare the total charges of cations and anions to ensure they are equal and maintain charge neutrality in seawater. Determine the number of significant figures they share in common.

Step-by-step solution

Determine the concentrations of the ions

To calculate the total charge for each ion, we first need their concentrations in 1.0 L of seawater. These concentrations can be found in Table 18.5 (not provided), which lists the concentrations of the six ions in seawater.

Calculate the moles of each ion in 1 L of seawater

Now that we know the concentrations of the ions, we can calculate the moles of each ion in 1 L of seawater by multiplying their concentrations (in moles/L) by the volume of seawater (1 L). Number of moles of a particular ion = (Concentration in moles/L) × (Volume of seawater in L)

Calculate the total charge of cations and anions

To calculate the total charge of cations and anions in Coulombs, we need to multiply the number of moles of each ion by the charge of that ion (in elementary charge units, e) and then by the elementary charge (1.602×10^{-19} C). Total charge = Number of moles × Charge of ion (in e) × 1.602×10^{-19} C Do this for all cations: Na+, Mg2+, Ca2+, and K+; and all anions: Cl- and SO4(2-). Then, sum up the charges for all cations and for all anions separately.

Compare the total charges of cations and anions and verify charge neutrality

After calculating the total charges of cations and anions, compare these charges to ensure that they are equal and maintain charge neutrality in seawater. Additionally, we are asked to determine to how many significant figures these total charges are equal. To do this, compare the charges of cations and anions and determine the number of significant figures they share in common. Following these steps, you should obtain the total charges of cations and anions in 1.0 L of seawater and confirm the charge neutrality of seawater.

Key concepts

Ionic Concentration

Understanding the concept of ionic concentration in seawater helps us appreciate the chemical balance that exists within it. Seawater contains various ions in different concentrations, typically expressed in moles per liter (mol/L).

These ions include cations, like sodium (Na⁺) and calcium (Ca²⁺), and anions, like chloride (Cl^-) and sulfate (SO₄^2-).

To calculate the charge from these ions, one must first know their concentrations.

• Concentration is simply how much of an ion is present in a given volume of seawater.
• This information provides the number of moles of each ion when multiplied by the volume of the solution, here indicated as 1 liter for simplicity.

Calculating ionic concentration becomes pivotal when determining the total charge.

In practical terms, Tables or reference data like Table 18.5 in the exercise, typically list these concentrations. Once identified, the concentration value serves as the first step in determining the ion's contribution to total charge.

Charge Neutrality

Charge neutrality is a fundamental rule in electrochemistry. It states that in any bulk solution, total positive (cationic) and negative (anionic) charges must be equal.

Seawater is a classic example of such a balanced system. Although it contains many types of ions, the overall positive and negative charges cancel out to maintain neutrality.

This concept ensures that each charge from a cation, like Na⁺, is balanced by an equal and opposite charge from an anion, like Cl^-.

• The importance of charge neutrality is immense in ensuring the stability of the solution.
• Without it, electrostatic forces would cause the solution to become unbalanced, pulling or repelling charged particles excessively.
• Balancing cations and anions allows biological processes, such as osmosis in marine life, to proceed smoothly without disturbances from charge discrepancies.

Calculating total charges from the cations and anions, then comparing them, is how we verify charge neutrality in a system like seawater.

Coulombs

Coulombs serve as the unit of electric charge in the International System of Units (SI). One Coulomb corresponds to the charge transported by a constant current of one ampere in one second.

In our seawater exercise, understanding Coulombs is essential for calculating the total charge of cations and anions. We convert moles of ions into Coulombs by multiplying by the charge per ion and a constant known as the elementary charge (1.602×10^-19 C).

This allows us to express the ion's charge quantitatively:

• A single Na⁺ ion carries an elementary charge equivalent to +1 e, so its total charge in Coulombs is given by its moles multiplied by 1.602×10^-19.
• For an ion like Mg²⁺, the same calculation involves multiplying the moles by a factor of 2 since it carries double the charge e (i.e., +2 e).

Understanding these conversions between moles, elementary charges, and Coulombs makes it possible to ensure the entire solution remains balanced, reflecting the core principle of charge neutrality.