Q3.128CP - Chemistry: Molecular Nature Of Matter And Change

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).

Step-by-Step Solution

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 1: 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:

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

Step 2: 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

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

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

Step 3: 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}$