(1) If 1280 g of a potassium molybdate is dissolved in 1980 g of water solvent,

Question

(1) If 1280 g of a potassium molybdate is dissolved in 1980 g of water solvent, calculate the boiling temperature of the solution. Consider if the solute is an electrolyte.
K2MoO4 = 238.13 g/mol; H2O = 18.015 g/mol
Melting Point = 0.00 C; Boiling Point = 100.00 C
Kf = 1.858 C/m; Kb = 0.512 C/m

(2) If 184 g of a sodium chlorate is dissolved in 1040 g of water solvent, calculate the magnitude (not the sign) of the boiling point elevation of the solution. Consider if the solute is an electrolyte.
NaClO3 = 106.44 g/mol; H2O = 18.015 g/mol
Melting Point = 0.00 C; Boiling Point = 100.00 C
Kf = 1.858 C/m; Kb = 0.512 C/m

(3) If 1567 g of a substance is dissolved in 2108 g of cyclohexane solvent, the boiling point of the solution is 88.78 C. Calculate the apparent molar mass (g/mol) of substance.
C6H12 = 84.156 g/mol
Melting Point = 6.55 C; Boiling Point = 80.74 C
Kf = 20.00 C/m; Kb = 2.79 C/m

(4) If 300 g of an ethyl benzoate is dissolved in 916 g of acetic acid solvent, calculate the freezing temperature (if below 0 C, include the sign) of the solution. Consider if the solute is an electrolyte.
C6H5CO2C2H5 = 150.18 g/mol; CH3COOH = 60.05 g/mol
Melting Point = 16.60 C; Boiling Point = 118.5 C
Kf = 3.59 C/m; Kb = 3.08 C/m

(5) If 61.1 g of an aluminum sulfate is dissolved in 113 g of water solvent, calculate the magnitude (not the sign) of the boiling point elevation of the solution. Consider if the solute is an electrolyte.
Al2(SO4)3 = 342.15 g/mol; H2O = 18.015 g/mol
Melting Point = 0.00 C; Boiling Point = 100.00 C
Kf = 1.858 C/m; Kb = 0.512 C/m

(6) If 757 g of a polyethylene glycol is dissolved in 5180 ml of water at 300 K, the solution has an osmotic pressure of 5.97 torr. Calculate the molar mass (g/mol) of the polyethylene glycol.
Gas Constant = 0.08206 L atm/mol K

I would like to know how to solve these types of equations. Thank you!

Explanation / Answer

1) molality = ( moles of solute x 1000 / mass of solvent (g) )

moles of solute = mass / molar mass

moles of solute = 1280 / 238.13

moles of solute = 5.375

molality = ( 5.375 x 1000 / 1980 )

molality = 2.7147

K2Mo04 ----> 2K+ + Mo042-

so i =3

we know that

dTb = i Kb x m

T - 100 = 3 x 0.512 x 2.7147

T -100= 4.169

T = 104.17

so the boiling temp is 104.17 C

2) molality = ( moles of solute x 1000 / mass of solvent (g) )

moles of solute = mass / molar mass

moles of solute = 184 / 106.44

moles of solute = 1.728

molality = ( 1.728 x 1000 / 1040 )

molality = 1.662

NaCl03 ----> Na+ + Cl03-

so i =2

we know that

dTb = i Kb x m

dTb = 2 x 0.512 x 1.662

dTb = 1.70

so the boiling point elevation is 1.70 C

3) dTb = i x Kb x m

for cyclohexane i = 1

88.78 - 80.74 = 2.79 x m

m = 2.8817

molality = ( moles of solute x 1000 / mass of solvent (g) )

2.8817 = ( moles of solute x 1000 / 2108 )

moles of solute = 6.0746

mass of solute / molar mass = 6.07466

1567 / molar mass = 6.07466

molar mass = 257.95

so the molar mass is 257.95 g

4) molality = ( moles of solute x 1000 / mass of solvent (g) )

moles of solute = mass / molar mass

moles of solute = 300 / 150.18

moles of solute = 1.9976

molality = ( 1.9976 x 1000 / 916 )

molality = 2.18

for ethyl benzoate i = 2

we know that

dTf = i Kf x m

118.5 - T = 2 x 3.59 x 2.18

T = 102.84

so the freezing temperature is 102.84 C

5) molality = ( moles of solute x 1000 / mass of solvent (g) )

moles of solute = mass / molar mass

moles of solute = 61.1 / 342.15

moles of solute = 0.178

molality = ( 0.178 x 1000 / 113 )

molality = 1.58

Al2(SO4)3 ----> 2Al+3 + 3S042-

so i =5

we know that

dTb = i Kb x m

dTb = 5 x 0.512 x 1.58

dTb = 4.0456

so the boiling point elevation is 4.0456 C

6) osmotic pressure = i C RT

for polyehtylene glycol i =1

P = CRT

5.97 torr = 0.007855 atm

0.007855 = C x 0.08206 x 300

C = 3.19 x 10-3

we know that

concentration = moles of solute x 1000 / volume of water

3.19 x 10-3 = moles of solute x 1000 / 5180

moles of solute = 0.00165

757 / molar mass = 0.00165

molar mass = 457992 g

so the molar mass is 457992 g

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