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Question: Given,\(10g\) of \(NaOH\) is mixed with \(36g\) of \({H_2}O\) . What is the mole fraction of \(NaOH\...

Given,10g10g of NaOHNaOH is mixed with 36g36g of H2O{H_2}O . What is the mole fraction of NaOHNaOH in solution?
A. 0.1250.125
B. 0.1110.111
C. 0.720.72
D. 0.50.5

Explanation

Solution

To figure the quantity of moles of any substance present in the example, we partition the given load of the substance by its molar mass. The mole portion is the quantity of moles of a specific part in the arrangement isolated by the absolute number of moles in the given arrangement.
By using the following formula,
No.ofmoles = MassMolarmassNo.{\text{ofmoles = }}\dfrac{{Mass}}{{Molar{\text{mass}}}}
Mole fraction = No. of moles of NaOHNo. of moles of NaOH + No. of moles of H2OMole{\text{ fraction = }}\dfrac{{No.{\text{ of moles of NaOH}}}}{{No.{\text{ of moles of NaOH + No}}{\text{. of moles of }}{{\text{H}}_2}O}}

Complete answer:
The given details are,
The mass of sodium hydroxide = 10g10g
The mass of water = 36g36g
We have to calculate the mole fraction of sodium hydroxide in solution.
Using the following expression,
First, we have to calculate the number of moles of sodium hydroxide, and water.
For sodium hydroxide,
No. of moles = MassMolar mass=10g40gNo.{\text{ of moles = }}\dfrac{{Mass}}{{Molar{\text{ mass}}}} = \dfrac{{10g}}{{40g}}
Where,
The molar mass of sodium hydroxide = 40g40g
Therefore,
The number of moles of sodium hydroxide = 0.25mol0.25mol .
For water,
No. of moles = MassMolar mass=36g18gNo.{\text{ of moles = }}\dfrac{{Mass}}{{Molar{\text{ mass}}}} = \dfrac{{36g}}{{18g}}
Where,
The molar mass of water = 18g18g
Therefore,
The number of moles of water = 2mol2mol .
Then, we have using the mole fraction formula,
Mole fraction = No. of moles of NaOHNo. of moles of NaOH + No. of moles of H2OMole{\text{ fraction = }}\dfrac{{No.{\text{ of moles of NaOH}}}}{{No.{\text{ of moles of NaOH + No}}{\text{. of moles of }}{{\text{H}}_2}O}}
Applying all the values in the above expression,
Mole fraction = 0.250.25+2Mole{\text{ fraction = }}\dfrac{{0.25}}{{0.25 + 2}}
On simplification we get,
Mole fraction = 0.1110.111
Therefore, the mole fraction of sodium hydroxide is 0.1110.111 .

So, the correct answer is “Option B”.

Note:
We have to know that the mole fraction isn't reliant upon the temperature. The data about the thickness of the stage isn't important to ascertain the mole portion. On account of an optimal gas blend, the mole division is addressed by the proportion of fractional strain to add up to the pressing factor of the combination. Mole part is supposed to be a unit-less and dimensionless articulation.