If 0.500 mol of each of the following solutes is dissolved in 2.0 L of water, which will cause the greatest increase in the boiling point of the solution?
A. KI
B. CO2
C. Na2SO4
D. NaCl
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na2so4
To determine which solute will cause the greatest increase in the boiling point of the solution, we need to consider the properties of the solute and its effect on boiling point elevation.
The boiling point elevation depends on the concentration of the solute and its properties, specifically its van't Hoff factor (i). The van't Hoff factor represents the number of particles that the solute dissociates into in solution.
To find the van't Hoff factor (i), we need to consider the chemical formula of each solute and how it dissociates in solution.
A. KI: Potassium iodide (KI) dissociates into two ions, K+ and I-. Therefore, i for KI is 2.
B. CO2: Carbon dioxide (CO2) does not dissociate into ions in solution. Therefore, i for CO2 is 1.
C. Na2SO4: Sodium sulfate (Na2SO4) dissociates into three ions: 2Na+, SO42-. Therefore, i for Na2SO4 is 3.
D. NaCl: Sodium chloride (NaCl) dissociates into two ions, Na+ and Cl-. Therefore, i for NaCl is 2.
Now let's calculate the molality (m) for each solute using the given information:
m = moles of solute / mass of solvent (in kg)
In this case, the mass of solvent is given as 2.0 L of water, which has a density of 1 kg/L.
For each solute, m = 0.500 mol / 2.0 kg = 0.250 mol/kg
Next, we can use the formula for boiling point elevation:
ΔTb = i * Kb * m
Where ΔTb is the boiling point elevation, Kb is the molal boiling point elevation constant, and m is the molality.
The constant Kb for water is 0.512 °C/m.
Now, let's calculate the boiling point elevation for each solute:
A. KI: ΔTb = 2 * 0.512 °C/m * 0.250 mol/kg = 0.256 °C
B. CO2: ΔTb = 1 * 0.512 °C/m * 0.250 mol/kg = 0.128 °C
C. Na2SO4: ΔTb = 3 * 0.512 °C/m * 0.250 mol/kg = 0.384 °C
D. NaCl: ΔTb = 2 * 0.512 °C/m * 0.250 mol/kg = 0.256 °C
From these calculations, we can see that Na2SO4 (option C) will cause the greatest increase in the boiling point of the solution with a value of 0.384 °C.
Therefore, the correct answer is option C: Na2SO4.