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Question: \[4.0\] gram of \(\text{NaOH}\) is contained in one decilitre of a solution. Calculate the following...

4.04.0 gram of NaOH\text{NaOH} is contained in one decilitre of a solution. Calculate the following in this solution. (i) Mole fraction of NaOH\text{NaOH} (ii) Molality of NaOH\text{NaOH} (iii) Molarity of NaOH\text{NaOH} (atomic weight of sodium = 23, oxygen =16, density of NaOH\text{NaOH} solution =1.0381.038 g/cm3\text{g/c}{{\text{m}}^{\text{3}}}).

Explanation

Solution

The molarity of a solution as a unit to express the concentration of the solution and can be defined as the number of moles of the solute present per litre of the solution. On the other hand, the molality of the solution can be defined as the number of moles of the solute present per Kg of the solvent.

Complete step by step answer:
The molecular weight of sodium hydroxide = [23+16+1]=40\left[ 23+16+1 \right]=40 grams. Hence one molar solution of sodium hydroxide should contain one mole of sodium hydroxide in one litre of water.
Now one mole of sodium hydroxide = 40 grams of sodium hydroxide = molecular weight of sodium hydroxide.
One decilitre = 0.10.1 litre
Therefore, according to the question,4.04.0 gram of NaOH\text{NaOH} is contained in 0.10.1 litre .
Therefore the number of moles of sodium hydroxide = 4.040=0.1\dfrac{4.0}{40}=0.1 moles in 0.10.1 litre water.
Number of moles in one litre water = 0.1×0.1=0.010.1\times 0.1=0.01(M) solution.
Hence the molarity of the solution is 0.01 (M)\text{0}\text{.01 }\left( \text{M} \right).
Molality of the solution = moles of the soluteweight of the solvent\dfrac{\text{moles of the solute}}{\text{weight of the solvent}} = 0.1100×1000=1\dfrac{0.1}{100}\times 1000=1. Hence the molality of the solution is 1 (m).
Mole Fraction of the solute in the solution is,
no. of moles of soluteno. of moles of the solute + no. of moles of the solvent\dfrac{\text{no}\text{. of moles of solute}}{\text{no}\text{. of moles of the solute + no}\text{. of moles of the solvent}}
Moles of the solvent = 10018\dfrac{100}{18}=5.555.55.
Therefore, mole fraction =0.10.1+5.55=0.017\dfrac{0.1}{0.1+5.55}=0.017.

Note:
The mole is a unit of measurement for that is equal to 6.023×10236.023\times {{10}^{23}} particles where the word “particles” refer to atoms, molecules, ions, and other subatomic particles. The mole is also equal to the molecular weight for compounds and the atomic weight for elements.