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Question: If \[5.85{\text{g}}\] of \[{\text{NaCl}}\] are dissolved in \[90{\text{g}}\] of water, the mole frac...

If 5.85g5.85{\text{g}} of NaCl{\text{NaCl}} are dissolved in 90g90{\text{g}} of water, the mole fraction of solute is:
A.0.01960.0196
B.0.010.01
C.0.10.1
D.0.20.2

Explanation

Solution

In order to calculate mole fraction of any substance in the mixture, we need to first calculate total moles present in the mixture of all substances and the moles of whose mole fraction is to be calculated.
Formula Used : mole fraction=moles of substancetotal moles present{\text{mole fraction}} = \dfrac{{{\text{moles of substance}}}}{{{\text{total moles present}}}}

Complete step by step answer:
A mole is the SI unit for the amount of substance. It is define as the amount of substance that contains as many entities as there are atoms in exactly 12g of C12{{\text{C}}^{12}} isotope. 1 mole is equivalent to NA{{\text{N}}_{\text{A}}} atoms, molecules, ions, electron or any entity. 1 mole is equivalent to molecular weight or atomic weight of substance. 1 mole is equivalent to the volume of 22.4L22.4{\text{L}} of a gas occupied at NTP.
First calculate the number of moles of the given substance in order to find mole fraction. Thereby, number of moles in 5.85g5.85{\text{g}} of NaCl{\text{NaCl}} can be given by:
moles of NaCl=massmolar mass=5.8558.5=0.1{\text{moles of NaCl}} = \dfrac{{{\text{mass}}}}{{{\text{molar mass}}}} = \dfrac{{5.85}}{{58.5}} = 0.1 .
Now the number of moles of water in 90g90{\text{g}} of water can be given by: mole of H2O=massmolar mass=9018=5{\text{mole of }}{{\text{H}}_2}{\text{O}} = \dfrac{{{\text{mass}}}}{{{\text{molar mass}}}} = \dfrac{{90}}{{18}} = 5 .
So, we can clearly see 0.1mol0.1{\text{mol}} of sodium chloride are dissolved in 5mol5{\text{mol}} of water.
Total number of moles in the solution will be: 5+0.1=5.15 + 0.1 = 5.1 .
Now, mole fraction of solute or sodium chloride can be given by: mole fraction=moles of substancetotal moles present=0.15.1=0.0196{\text{mole fraction}} = \dfrac{{{\text{moles of substance}}}}{{{\text{total moles present}}}} = \dfrac{{0.1}}{{5.1}} = 0.0196 .

Thus, the correct option is A.

Note:
Mole fraction is a unit less quantity. Molality and mole fraction does not depend on volume. According to Avogadro law, equal volume of all gases under similar conditions of temperature and pressure contain equal numbers of molecules. NTP stands for normal temperature and pressure=293.15K temperature and 1atm pressure = 293.15{\text{K temperature and }}1{\text{atm pressure}} and STP stands for standard temperature and pressure=273K temperature and 1bar pressure = 273{\text{K temperature and }}1{\text{bar pressure}}.