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Solution:
1) The given molality means 4.500 mol dissolved in 1.000 kg of water. Determine the mass of each component:
H2SO4 ---> (4.500 mol) (98.078 g/mol) = 441.351 g
H2O ---> 1.000 kg = 1000. g
2) Determine mass percentages:
1000. g + 441.351 g = 1441.351 g (total mass of the solution)
H2O ---> 1000. g / 1441.351 g = 69.38%
H2SO4 ---> 100 - 69.38 = 30.62%
3) Determine mole fraction:
H2SO4 ---> 4.500 mol
H2O ---> 1000. g / 18.015 g/mol = 55.509 mol
55.509 mol + 4.500 mol = 60.009 mol
H2SO4 ---> 1 - 0.9250 = 0.0750
H2O ---> 55.509 mol / 60.009 mol = 0.9250
4) Determine the molarity:
1441.351 g / 1.122 g/mL = 1296.179 mL = 1.296179 L
4.500 mol / 1.296179 L = 3.472 M
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