Considering the definition of mole fraction, the mole fraction of MgCl₂ in a solution created by dissolving 132.1g of MgCl₂ in 175mL of water is 0.125.
Mole fraction
The molar fraction is a way of measuring the concentration that expresses the proportion in which a substance is found with respect to the total moles of the solution.
This case
First you must know the number of moles of each compound. To do this, define:
- The molar mass of substance is a property defined as its mass per unit quantity of substance, in other words, molar mass is the amount of mass that a substance contains in one mole. In this case the molar mass of MgCl₂ is 95.21 g/mole and the molar mass of water is 18 g/mole.
- Density is the ratio of the weight (mass) of a substance to the volume it occupies. In this case the density of the water is 1 g/mL.
So, the number of moles of each compound can be calculated as:
- moles of MgCl₂= 132.1 g×[tex]\frac{1 mole}{95.21 g}[/tex]= 1.387 moles
- moles of water= 175 mL× [tex]\frac{1 g}{1 mL}[/tex]= 175 g× [tex]\frac{1 mole}{18 g}[/tex]= 9.722 moles
Then the total number of moles is:
total number of moles= moles of MgCl₂ + moles of water
total number of moles= 1.387 moles + 9.722 moles
total number of moles= 11.109 moles
Finally, the mole fraction of MgCl₂ can be calculated as:
[tex]mole fraction of MgCl_{2}= \frac{number of moles of MgCl_{2}}{total number of moles}[/tex]
[tex]mole fraction of MgCl_{2}= \frac{1.387 moles}{11.109 moles}[/tex]
mole fraction of MgCl₂= 0.125
In summary, the mole fraction of MgCl₂ in a solution created by dissolving 132.1g of MgCl₂ in 175mL of water is 0.125.
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