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

Expert verified
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

01

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.
02

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)
03

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.
04

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.

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