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A solution containing 18 g of non volatile solute in 200 g of water freezes at 272.07 k calculate molecular mass of solute

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A solution containing 18g of non volatile solute in 200g of water freezes at 272.07K.calculate molar mass of the solute

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sailajareddykakarla Ambitious

Molar mass of the solute is 180

here kf=1.86

change in freezing point is 0.93

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BarrettArcher Ambitious

Answer : The molar mass of the solute is 155 g/mole.

Solution : Given,

Mass of solute = 18 g

Mass of solvent = 200 g

Initial temperature = 272.07 K

Freezing point of water = 273.15 K (final temperature)

Formula used :

\Delta T_f=k_f\times m

where, m is molality

\Delta T_f=k_f\times m\\(T_{final}-T_{initial})=k_f\times \frac{w_{solute}}{M_{solute}\times w_{solvent}}\\M_{solute}=\frac{k_f\times w_{solute}}{w_{solvent}\times (T_{final}-T_{initial})}

where,

K_f = freezing point constant of water = 1.86 K kg/mole

w_{solute} = mass of solute

w_{solvent} = mass of solvent

M_{solute} = molar mass of solute

T_{initial} = initial temperature

T_{final} = final temperature

Now put all the given values in this formula, we get the molar mass of solute.

M_{solute}=\frac{(1.86Kkg/mole)\times (18g)}{(200g)\times (273.15K-272.07K)}=0.155kg/mole=155g/mole (1kg=1000g)

Therefore, the molar mass of the solute is 155 g/mole.

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