When 14.3 g of a certain molecular compound X are dissolved in 85.0 g of benzene C6H6, the freezing point of the solution is measured to be 0.5 °C. Calculate the molar mass of X. molal freezing point depression constant (Kf)°C·kg·mol−1 of benzen is 5.07 If you need any additional information on benzene, use only what you find in the ALEKS Data resource. Also, be sure your answer has a unit symbol, and is rounded to 2 significant digits.

Question
Asked Nov 27, 2019
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When 14.3 g of a certain molecular compound X are dissolved in 

85.0 g of benzene C6H6, the freezing point of the solution is measured to be 0.5 °C. Calculate the molar mass of X.
 
molal freezing point depression constant (Kf)
°C·kg·mol−1 of benzen is 5.07

 

If you need any additional information on benzene, use only what you find in the ALEKS Data resource. Also, be sure your answer has a unit symbol, and is rounded to 

2

 significant digits.

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Expert Answer

Step 1

The depression in the freezing point refers to a phenomenon which is used to describe the effect of addition of solute to a given solvent that results in the lowering of the freezing point of the solvent. The formula is as follows:

AT,=K¢m
AT, is the depression in freezing point
K is the freezing point molar constant of solvent
m is the molality of the solution
Number of moles of solute
m=-
Mass of solvent in kg
help_outline

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AT,=K¢m AT, is the depression in freezing point K is the freezing point molar constant of solvent m is the molality of the solution Number of moles of solute m=- Mass of solvent in kg

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Step 2

In the given problem, the mass of solute X is given to be 14.3 g.

The mass of solvent benzene is given to be 85 g=0.085 kg.

The molal freezing point depression constant is given to be 5.07 oC kg mol-1.

The freezing point of the solution is given to be 0.5 0C.

The freezing point of pure benzene is 5.5oC.

The depression in freezing point can be calculated as follows:

ΔΤ, -Τ .
-T
fpure solvent)f(solution)
=5.5°C-0.5°C
-5°C
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ΔΤ, -Τ . -T fpure solvent)f(solution) =5.5°C-0.5°C -5°C

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Step 3

The molar mass of compound X can ...

AT =K2m
Mass of solute
5°C=5.07°C.kg.molax.
Molar mass of solute Mass of solvent (in kg)
14.3g
=5.07°C.kg.mol
Molar mass of solute 0.085 kg
14.3g
5°CX0.085 kg
Molar mass of solute=5.07°C.kg.mol1x-
-170.590 g/mol
help_outline

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AT =K2m Mass of solute 5°C=5.07°C.kg.molax. Molar mass of solute Mass of solvent (in kg) 14.3g =5.07°C.kg.mol Molar mass of solute 0.085 kg 14.3g 5°CX0.085 kg Molar mass of solute=5.07°C.kg.mol1x- -170.590 g/mol

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