Question

Seawater is approximately \(4.0 \%\) by mass dissolved ions, \(85 \%\) of which are from \(\mathrm{NaCl}\). (a) Find the mass \(\%\) of \(\mathrm{NaCl}\) in seawater. (b) Find the mass \% of \(\mathrm{Na}^{+}\) ions and of \(\mathrm{Cl}^{-}\) ions in seawater.

Short answer

The mass % of NaCl in seawater is 3.4%. The mass % of Na+ ions is 1.7%, and the mass % of Cl- ions is 1.7%.

Step-by-step solution

Understanding the Problem

Seawater has a total dissolved ions content of 4.0% by mass. Out of this, 85% are from NaCl. We need to find the mass percentage of NaCl in seawater, and then the mass percentages of Na+ and Cl- ions separately.

Calculate the Mass % of NaCl

To find the mass % of NaCl in seawater, multiply the total mass % of dissolved ions (4.0%) by the proportion that is NaCl (85%). This can be expressed as: \[ \text{Mass % of NaCl} = 4.0\text{\text{%}} \times 0.85 = 3.4\text{\text{%}}. \]

Calculate the Mass % of Na+ and Cl- Ions

NaCl dissociates into Na+ and Cl- ions in a 1:1 ratio. Therefore, the mass % of Na+ and Cl- will each be half of the mass % of NaCl in seawater. We can calculate this as: \[ \text{Mass % of Na+} = \frac{3.4\text{\text{%}}}{2} = 1.7\text{\text{%}} \] and \[ \text{Mass % of Cl-} = \frac{3.4\text{\text{%}}}{2} = 1.7\text{\text{%}}. \]

Key concepts

Mass Percentage Calculation

Mass percentage is a way to express the concentration of an element or compound in a mixture. To calculate it, you need to know the mass of the component and the total mass of the mixture. Then, use the formula:

\[ \text{Mass Percentage} = \frac{\text{Mass of the Component}}{\text{Total Mass of the Mixture}} \times 100 \]
This formula gives the percentage of the mass that is due to the specified component. In our problem, seawater contains 4.0% by mass dissolved ions. To find the mass percentage of \(\text{NaCl}\) in seawater, multiply the total mass percent of dissolved ions (4.0%) by the proportion of \(\text{NaCl}\) (85%):

\[ \text{Mass \% of \text{NaCl}} = 4.0\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{%}}}}}}}}}}}}}}}}} \times 0.85 = 3.4\text{\text{%}}. \]
So, \(\text{NaCl}\) makes up 3.4% of the seawater by mass.

Dissociation of NaCl

Dissociation is the process in which an ionic compound separates into its ions when dissolved in a solution like water. Sodium chloride (NaCl) dissociates completely in water to form sodium ions (Na+) and chloride ions (Cl-). The chemical equation for the dissociation of \(\text{NaCl}\) is:

\[ \text{NaCl} (s) \rightarrow \text{Na}^{+} (aq) + \text{Cl}^{-} (aq) \]
This means that one mole of \(\text{NaCl}\) will produce one mole of \(\text{Na}^{+}\) ions and one mole of \(\text{Cl}^{-}\) ions in solution. Because of this 1:1 ratio, the concentrations of \(\text{Na}^{+}\) and \(\text{Cl}^{-}\) ions are equal in the solution.

Ion Concentration in Seawater

Knowing the mass percentage of \(\text{NaCl}\) in seawater, we can find the mass percentages of \(\text{Na}^{+}\) and \(\text{Cl}^{-}\) ions. Since \(\text{NaCl}\) dissociates into \(\text{Na}^{+}\) and \(\text{Cl}^{-}\) ions in a 1:1 ratio, the mass percentage of each ion will be half of the mass percentage of \(\text{NaCl}\) in seawater.

Therefore, we can use the following calculations:

\[ \text{Mass \% of \text{Na}^{+}} = \frac{3.4\text{\text{\text{\text{\text{\text{\text{%}}}}}}}}}{2} = 1.7\text{\text{\text{\text{\text{\text{\text{%}}}}}}}. \]

and

\[ \text{Mass \% of \text{Cl}^{-}} = \frac{3.4\text{\text{\text{\text{\text{\text{\text{%}}}}}}}}}{2} = 1.7\text{\text{\text{\text{\text{\text{%}}}}}}. \]

This shows that both \(\text{Na}^{+}\) and \(\text{Cl}^{-}\) ions each make up 1.7% of the seawater by mass. Understanding these calculations helps in determining the concentration of ions, which is crucial for various applications in chemistry and environmental science.