Calculate the molality of an aqueous solution that contains 31.600 % (w/w) in KCN.?

Question

Calculate the molality of an aqueous solution that contains 31.600 % (w/w) in KCN. ?

Calculate the mole fraction of KCN in the solution described above (31.600 % (w/w) in KCN). ?

Calculate the mole fraction of water in the solution described in the previous two parts (31.600 % (w/w) in KCN). ?

i need these answers for my test review...please help me out....

Answer 1

Molarity (note spelling!) is defined as the number of moles of a substance per litre of water.

Lets say you have 1 kg of this solution.
Then you know that it is 36.1% (by weight) KCN and therefore 63.9% water. (The "aqueous" tells you that the KCN is dissolved in water).

To answer the first question I think we need to assume that the solution has the same density as water, ie 1 kg = 1 Litre.

1 kg of the solution contains 316 g of KCN.
Work out the number of moles of KCN.

Number moles = mass / molar mass
Molar Mass KCN = the sum of the atomic weights from the periodic table
Molar Mass KCN = 39.1+12.0+14.0 = 65.1 g
mass KCN = 316 g
Number moles KCN = 316/65.1 = 4.85 moles

So, in our 1 kg (1 Litre) sample we have 4.85 moles.
Therefore it is a 4.85 M solution.

The mole fraction of KCN = number moles KCN / Total number moles in the solution

The mole fraction of KCN = number moles KCN / (number moles KCN + number of moles water)

We need to determine the number of moles of water in the solution. - use the same method as above.
number moles water = mass water / molar mass water
Water is H20, so molar mass water = 1+1+16 = 18 g

If we have 31.6% KCN, we have 100 - 31.6% = 68.4% water
Again, in a 1 kg sample we have 684 g water

number moles water = mass water / molar mass water
number moles water = 684 / 18 = 38 moles

Mole fraction of KCN = number moles KCN / (number moles KCN + number of moles water)
The mole fraction of KCN = 4.85 / (4.85+ 38) = 0.113 or 11.3 mol %

Then, for the last part, the mole fraction of water = 1 - mole fraction of KCN
Mole fraction water = 1-0.113 = 0.887 or 88.7 mol%

Good luck :)

Answer 2

Molality is the moles of substance per kg of solvent (not solution). The weight of the solution will be weight solute plus weight solvent. Wslv + Wsol = Wsln. Your substance weight is 31.6% of this, or 0.316*(Wslv + Wsol). The number of moles is 0.316*(Wslv + Wsol)/mm(KCN) = 0.316*(Wslv + Wsol)/65.12. The molality is the amount of this substance in 1kg of solvent which is [1000/(Wslv+Wsol)]*0.316*(Wslv + Wsol)/65.12 = 1000*0.316/65.12 = 4.853 molal.

1 kg of water contains 1000/18 moles = 55.6 moles of water, and that is mixed with 4.853 moles of KCN. The mole fraction of KCN is therefore 4.853/(55.6+4.853) (moles of KCN divided by moles of both components).

The mole fraction of water is then 55.6/(55.6+4.853)