2 molal urea solution is diluted from 2 kg to 5 kg by addition of water calculate molality of the diluted solution.

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Solution

Molar mass CO(NH2)2 = 60.06g/mol
I think that a good place to start is to make a 2m CO(NH2)2 solution:
A 2.0m solution contains 2 mol CO(NH2)2 dissolved in 1.0kg water.
Mass of 2 mol CO(NH2)2 = 60.062 =
120.12g dissolved in 1.0kg = 1,000g water
Total mass of 2.0m solution = 1,120.12g
2kg of this solution will contain :
Mass CO(NH2)2 =
2000/1120.12120.12 = 214.48g CO(NH2)2
The 2.0kg of solution contains :
214.48g CO(NH2)2 and
1,785.52g H2O
You now increase mass of solution to 5.0kg –
you add 3000g water
Solution now is
214.48g CO(NH2)2
4,785.52g H2O
Mass of CO(NH2)2 in 1000g H2O =
1000/4785.52*214.48 = 44.82 g CO(NH2)2
Therefore 44.82g CO(NH2)2 dissolved in 1.0kg water.
Moles of CO(NH2)2 =
44.82/60.06 =
0.746 moles CO(NH2)2 per kg water
Molality of solution = 0.75m

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