Question

Seawater is approximately 4.0% by mass dissolved ions. About 85% of the mass of the dissolved ions is from NaCl.

(a) Find the mass % of NaCl in seawater.

(b) Find the mass % of Na+ions and of Cl-ions in seawater.

(c) Find the molarity of NaCl in seawater at 150C (d of seawater at 150C = 1.025 g/mL).

Short answer

Answer

(a) Mass percent of NaCl is 3.4%

(b) Mass percent of Na+ions are 1.3%. Mass percent of Cl-ions are 2.1%

(c) Molarity of NaCl in seawater is 0.05817 mol

Step-by-step solution

Calculating mass percent

Mass dissolved ion in seawater is 4.0%

Mass percent of dissolved ion in sea water from NaCl is 85%

Mass percent of NaCl is:

$\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\%}\mathbf{}\mathit{i}\mathit{o}\mathit{n}\mathit{s}\mathbf{}\mathbf{\times }\mathbf{}\frac{\mathbf{85}\mathbf{\%}\mathbf{}\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{s}\mathbf{}\mathbf{N}\mathbf{A}\mathbf{C}\mathbf{l}}{\mathbf{100}\mathbf{\%}\mathbf{}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{s}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{4}\mathbf{}\mathit{m}\mathit{a}\mathit{s}\mathit{s}\mathbf{}\mathbf{\%}\mathbf{}\mathit{N}\mathit{a}\mathit{C}\mathit{l}$

Calculating mass percent of both ions

To find mass percent of both ions in 3.4 mass % NaCl, divide mass of individual ions to mass of NaCl

Molar mass of Na = 22.99 gm

Molar mass of NaCl = 58.44 gm

$$\begin{gathered} \mathbf{\%}\mathbf{}\mathit{N}{\mathit{a}}^{\mathbf{+}}\mathbf{}\mathit{i}\mathit{o}\mathit{n}\mathit{s}\mathbf{=}\left(3.4\%NaCl\right)\left(\frac{22.99gN{a}^{+}}{58.44NaCl}\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{3}\mathbf{\%}\mathbf{}\mathit{N}{\mathit{a}}^{\mathbf{+}}\mathbf{}\mathit{i}\mathit{o}\mathit{n}\mathit{s} \end{gathered}$$

$$\begin{gathered} \mathbf{\%}\mathbf{}\mathit{C}{\mathit{l}}^{-}\mathbf{}\mathit{i}\mathit{o}\mathit{n}\mathit{s}\mathbf{=}\mathbf{(}\mathbf{3}\mathbf{.}\mathbf{4}\mathbf{}\mathbf{\%}\mathbf{}\mathbf{NaCl}\mathbf{)}\mathbf{\left(}\frac{\mathbf{35}\mathbf{.}\mathbf{45}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}^{\mathbf{-}}}{\mathbf{58}\mathbf{.}\mathbf{44}\mathbf{}\mathbf{NaCl}}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{1}\mathbf{\%}\mathbf{}\mathit{C}{\mathit{l}}^{\mathbf{+}}\mathbf{}\mathit{i}\mathit{o}\mathit{n}\mathit{s} \end{gathered}$$

Calculating molarity

Molarity = number of mol of solute / volume of solution(seawater)

Mass percent of NaCl is 3.4%. So, mass of NaCl in 100 g of seawater is 3.4 gm.

$\begin{array}{ccc}\mathbf{M}\mathbf{o}\mathbf{l}\mathbf{e}\mathbf{s}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{l}& \mathbf{=}& \mathbf{3}\mathbf{.}\mathbf{4}\mathbf{}\mathbf{g}\mathbf{}\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{l}\mathbf{}\mathbf{\times }\frac{\mathbf{1}\mathbf{}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{}\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{l}}{\mathbf{58}\mathbf{.}\mathbf{44}\mathbf{}\mathbf{g}\mathbf{}\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{l}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{05817}\mathbf{}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{}\mathbf{N}\mathbf{A}\mathbf{C}\mathbf{l}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\\ \mathbf{V}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{m}\mathbf{e}\mathbf{}\mathbf{L}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{100}\mathbf{}\mathbf{g}\mathbf{m}\mathbf{}\mathbf{s}\mathbf{e}\mathbf{a}\mathbf{w}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{r}& \mathbf{=}& \frac{\mathbf{100}\mathbf{}\mathbf{g}\mathbf{m}\mathbf{}\mathbf{s}\mathbf{e}\mathbf{a}\mathbf{w}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{r}}{\mathbf{1}\mathbf{.}\mathbf{025}\mathbf{}\mathbf{g}\mathbf{m}\mathbf{}\mathbf{s}\mathbf{e}\mathbf{a}\mathbf{w}\mathbf{a}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{r}}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{09756}\mathbf{}\mathbf{L}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\\ \mathbf{M}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{l}& \mathbf{=}& \frac{\mathbf{M}\mathbf{o}\mathbf{l}\mathbf{e}\mathbf{s}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{l}}{\mathbf{V}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{m}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{s}\mathbf{e}\mathbf{a}\mathbf{w}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{r}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\\ & \mathbf{=}& \frac{\mathbf{0}\mathbf{.}\mathbf{05817}\mathbf{}\mathbf{m}\mathbf{o}\mathbf{l}}{\mathbf{0}\mathbf{.}\mathbf{09756}\mathbf{}\mathbf{L}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{05963}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{60}\mathbf{}\mathbf{M}\mathbf{}\mathbf{N}\mathbf{a}\mathbf{C}\mathbf{l}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\end{array}$