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10) In order to make spaghetti cook faster, a chef adds salt to water. How many moles of salt would he need to add to 1.0 kg water to make the water boil at 105 C? The Kb for water is 0.25°C/m. Assume i 2 for NaCl

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zoexoe
The answer is 4.9 moles.
Solution: 
Using the equation for boiling point elevation Δt,
     Δt = i Kb m 
we can rearrange the expression to solve for the molality m of the solution:
     m = Δt / i Kb 

Since we know that pure water boils at 100 °C, and the Ebullioscopic constant Kb for water is 0.512 °C·kg/mol, 
     m = (105°C - 100°C) / (2 * 0.512 °C·kg/mol)
         = 4.883 mol/kg 

From the molality m of the solution of salt added in a kilogram of water, we can now find the number of moles of salt: 
     m = number of moles / 1.0kg
     number of moles = m*1.0kg 
                                  = (4.883 mol/kg) * (1.0kg)
                                  = 4.9 moles

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