객관식
Arrange the following compounds in order of increasing boiling point: CH4, NH3, H2O, CO2.
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14. Solutions
Boiling Point Elevation
객관식
Which aqueous solution has the highest boiling point, assuming all solutions are ideal and have the same concentration of solute particles (same molality of dissolved solute units)?
A
sodium chloride ()
B
potassium sulfate ()
C
glucose (, non-electrolyte)
D
calcium chloride ()
검증된 단계별 안내1
Recall that the boiling point elevation of a solution depends on the number of solute particles in solution, which is given by the formula: \(\Delta T_b = i K_b m\), where \(\Delta T_b\) is the boiling point elevation, \(i\) is the van't Hoff factor (number of particles the solute dissociates into), \(K_b\) is the boiling point elevation constant of the solvent, and \(m\) is the molality of the solution.
Identify the van't Hoff factor \(i\) for each solute: sodium chloride (NaCl) dissociates into Na\(^+\) and Cl\(^-\), so \(i = 2\); potassium sulfate (K\(_2\)SO\(_4\)) dissociates into 2 K\(^+\) and 1 SO\(_4^{2-}\), so \(i = 3\); glucose (C\(_6\)H\(_{12}\)O\(_6\)) is a non-electrolyte and does not dissociate, so \(i = 1\); calcium chloride (CaCl\(_2\)) dissociates into Ca\(^{2+}\) and 2 Cl\(^-\), so \(i = 3\).
Since all solutions have the same molality (\(m = 1.0\) m) and are in the same solvent (water, so \(K_b\) is constant), the boiling point elevation depends directly on the van't Hoff factor \(i\).
Compare the values of \(i\) for each solute: NaCl has \(i=2\), K\(_2\)SO\(_4\) has \(i=3\), glucose has \(i=1\), and CaCl\(_2\) has \(i=3\). Both K\(_2\)SO\(_4\) and CaCl\(_2\) have the highest \(i\) value of 3.
Consider that the problem states the correct answer is 1.0 m CaCl\(_2\). This is because CaCl\(_2\) dissociates into 3 ions and typically has a stronger effect on colligative properties due to complete dissociation and ion interactions, leading to the highest boiling point elevation among the given options.
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