Question

In absorption refrigeration systems, a two-phase equilibrium mixture of liquid ammonia \(\left(\mathrm{NH}_{3}\right)\) and water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) is frequently used. Consider a liquid-vapor mixture of ammonia and water in equilibrium at \(30^{\circ} \mathrm{C}\). If the composition of the liquid phase is 60 percent \(\mathrm{NH}_{3}\) and 40 percent \(\mathrm{H}_{2} \mathrm{O}\) by mole numbers, determine the composition of the vapor phase of this mixture. Saturation pressure of \(\mathrm{NH}_{3}\) at \(30^{\circ} \mathrm{C}\) is \(1167.4 \mathrm{kPa}\).

Short answer

Answer: The composition of the vapor phase is approximately 99.76% NH3 and 0.24% H2O.

Step-by-step solution

Calculate mole fractions of liquid phase components

The given composition of the liquid phase is 60% NH3 (ammonia) and 40% H2O (water). We need to convert these percentages into mole fractions. The mole fractions of NH3 and H2O in the liquid phase are: Mole fraction of NH3 (liquid) = 0.60 Mole fraction of H2O (liquid) = 0.40

Calculate the partial pressures of each component using Raoult's Law

Using Raoult's Law, the partial pressure of each component in the vapor phase can be calculated as: Partial pressure of NH3 (vapor) = Mole fraction of NH3 (liquid) × Saturation pressure of NH_3 at 30°C Partial pressure of H2O (vapor) = Mole fraction of H2O (liquid) × Saturation pressure of H2O at 30°C Given that the saturation pressure of NH3 at 30°C is 1167.4 kPa, we can calculate the partial pressure of ammonia in the vapor phase: Partial pressure of NH3 (vapor) = 0.60 × 1167.4 kPa Partial pressure of NH3 (vapor) ≈ 700.44 kPa

Look up the saturation pressure of water at 30°C

In order to calculate the partial pressure of water in the vapor phase, we need the saturation pressure of water at 30°C. We can find this value in a steam table or online database. The saturation pressure of H2O at 30°C is approximately 4.25 kPa.

Calculate the partial pressure of water in the vapor phase

Using the saturation pressure of water at 30°C, we can now calculate the partial pressure of water in the vapor phase: Partial pressure of H2O (vapor) = 0.40 × 4.25 kPa Partial pressure of H2O (vapor) ≈ 1.70 kPa

Calculate the total pressure of the vapor phase

Add the partial pressures of NH3 and H2O to find the total pressure of the vapor phase: Total pressure (vapor) = Partial pressure of NH3 (vapor) + Partial pressure of H2O (vapor) Total pressure (vapor) ≈ 700.44 kPa + 1.70 kPa Total pressure (vapor) ≈ 702.14 kPa

Calculate the mole fractions of each component in the vapor phase

Finally, we can find the mole fractions of each component in the vapor phase by dividing their partial pressures by the total pressure: Mole fraction of NH3 (vapor) = Partial pressure of NH3 (vapor) ÷ Total pressure (vapor) Mole fraction of NH3 (vapor) ≈ 700.44 kPa ÷ 702.14 kPa Mole fraction of NH3 (vapor) ≈ 0.9976 Mole fraction of H2O (vapor) = Partial pressure of H2O (vapor) ÷ Total pressure (vapor) Mole fraction of H2O (vapor) ≈ 1.70 kPa ÷ 702.14 kPa Mole fraction of H2O (vapor) ≈ 0.0024 So the composition of the vapor phase of the mixture is approximately 99.76% NH3 and 0.24% H2O.