An aqueous solution of a solute (molar mass = 150 g/mol ) has a density of 1.4 g/mL . If the ratio of its molarity to its molality is 0.8 , what is the molarity of the solution?

Step-by-step solution

Let the molarity be M and the molality be m . Given that M m = 0.8 , we have m = M 0.8 = 1.25 M . The relationship between molality ( m ), molarity ( M ), density ( d in g/mL), and molar mass of solute ( M_w in g/mol) is: m = 1000 M 1000 d - M M_w Substitute the given values ( d = 1.4 g/mL , M_w = 150 g/mol , and m = 1.25 M ): 1.25 M = 1000 M 1000 1.4 - M 150 Assuming M 0 , we can divide both sides by M : 1.25 = 1000 1400 - 150 M 1400 - 150 M = 1000 1.25 1400 - 150 M = 800 150 M = 600 M = 4 M . Answer: 4 M