Hydrogen bromide, HBr, is a strong electrolyte in water. What is the boiling point elevation ATb) of a solution containing 125 g of HBr in 1.75 kg of water? The molar mass of HBr is 80.9 g/mol, and the boiling point elevation constant (K6) of water is 0.512°C/m.
1. molality of the solution
2. boiling point elevation of the solution
Give your answers in three significant figures None
The Correct Answer and Explanation is :
When hydrogen bromide (HBr) dissolves in water, it dissociates completely into H⁺ and Br⁻ ions, making it a strong electrolyte. This dissociation influences the solution’s colligative properties, such as boiling point elevation.
1. Molality of the Solution:
Molality (m) is defined as the number of moles of solute per kilogram of solvent. To calculate the molality of the HBr solution:
- Moles of HBr: Given 125 g of HBr and its molar mass of 80.9 g/mol: [
\text{Moles of HBr} = \frac{125\, \text{g}}{80.9\, \text{g/mol}} \approx 1.544\, \text{mol}
] - Mass of Water: The solvent is water with a mass of 1.75 kg.
- Molality (m): Calculated as moles of solute per kilogram of solvent: [
m = \frac{1.544\, \text{mol}}{1.75\, \text{kg}} \approx 0.883\, \text{mol/kg}
]
2. Boiling Point Elevation (ΔTb):
The boiling point elevation is given by the formula:
[
\Delta T_b = i \times K_b \times m
]
Where:
- i is the van ‘t Hoff factor, representing the number of particles the solute dissociates into. For HBr, i = 2 (H⁺ and Br⁻).
- K_b is the ebullioscopic constant of the solvent. For water, K_b = 0.512 °C·kg/mol.
- m is the molality of the solution.
Calculating ΔTb:
[
\Delta T_b = 2 \times 0.512\, \text{°C·kg/mol} \times 0.883\, \text{mol/kg} \approx 0.905\, \text{°C}
]
Therefore, the boiling point of the solution increases by approximately 0.905 °C above the boiling point of pure water. Since the boiling point of pure water is 100 °C, the boiling point of this solution would be approximately 100.91 °C.
Explanation:
Boiling point elevation is a colligative property, meaning it depends on the number of solute particles in the solution, not their identity. When a non-volatile solute like HBr is added to a solvent like water, it dissociates into ions, increasing the number of particles in the solution. This disruption of the solvent’s vapor pressure requires a higher temperature to reach the boiling point, resulting in boiling point elevation. citeturn0search2
In this scenario, the complete dissociation of HBr into H⁺ and Br⁻ ions contributes to the observed increase in boiling point, demonstrating the effect of solute particle concentration on the colligative properties of solutions.