If 4 g of $N a O H$ dissolves in $36$ g of $H_{2} O$ , calculate the mole fraction of each component in the solution. Also, determine the molarity of solution (specific gravity of the solution is $1$ ).

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Solution

Analyzing the data and solution

There are two components in the $N a O H$
Soloution, $N a O H$ (solute) and $H_{2} O$ (solvent)

Mass of $N a O H = 4 g$
Mass of $H_{2} O = 36 g$

Formula for mole fraction is:

$Mole fraction=no. of moles of a componenttotal number of moles$

Number of moles = $\frac{g i v e n m a s s}{m o l a r m a s s}$

So, by using above equation we can find:
Molar mass of water = $18 g / m o l$

Number of moles $H_{2} O = \frac{g i v e n m a s s}{m o l a r m a s s} = \frac{36 g}{18 g / m o l} = 2 m o l e s$

Molar mass of $N a O H = 40 g / m o l$

Number of moles $N a O H = \frac{4 g}{40 g / m o l} = 0.1 m o l e s$

Therefore, Total number of moles = $2 + 0.1 = 2.1$ moles

$Mole fraction of H2O$ = $\frac{n o . o f m o l e s H_{2} O}{t o t a l n u m b e r o f m o l e s}$
= $\frac{2}{2.1} = 0.952$

Similarly , Mole fraction of $N a O H$ =

= $\frac{m o l e s o f N a O H}{t o t a l n u m b e r o f m o l e s} = \frac{0.1}{2.1} = 0.048$

Specific gravity is the ratio of density of
$N a O H$ solution divided by density of water at $4^{\circ} C$ .

Density of $N a O H$ solution = specific gravity $\times (d e n s i t y o f w a t e r (a t 4^{\circ} C))$

Hence, the density of $N a O H i s 1 g m L^{- 1}$ . (because specific gravity 1, density of = water $1 g / m l)$

Mass of the solution is the sum of mass of
$N a O H$ and mass of $H_{2} O = 4 g + 36$
= $40 g$

So, Volume of Soution = $\frac{m a s s}{d e n s i t y}$

Volume of Soution = $\frac{40 g}{1 g / m l} = 40 m l$

We, already know
moles of solute = $0.1 m o l$

$M o l a r i t y = \frac{(m o l e s o f s o l u t e) \times 1000}{v o l u m e o f s o l u t i o n (i n m l)}$

Molarity = $((0.1) \times 1000) / (40 m l)$
= $2.5 M$

Hence from the above analysis it is concluded
that the mole fraction of each component in
the solution is $0.048 f o r N a O H$ and $0.952 f o r H_{2} O$

Whereas the molarity of the solution is $2.5 M$

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Magnetic Properties

Standard XII Chemistry

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If 4 g of NaOH dissolves in 36 g of H2O, calculate the mole fraction of each component in the solution. Also, determine the molarity of solution (specific gravity of the solution is 1).

If 4 g of $N a O H$ dissolves in $36$ g of $H_{2} O$ , calculate the mole fraction of each component in the solution. Also, determine the molarity of solution (specific gravity of the solution is $1$ ).