Question

A dilute aqueous solution of sulfuric acid at 25°C is used to absorb ammonia in a continuous reactor, thereby producing ammonium sulfate, a fertilizer:

2NH3(g) + H2SO4(aq) ? (NH4)2SO4(aq)

a)If the ammonia enters the absorber at 75°C. the sulfuric acid enters at 25°C, and the product solution emerges at 25°C, how much heat must be withdrawn from the unit per mol of (NH4)2SO4 produced?

b)Estimate the final temperature if the reactor of part (a) is adiabatic and the product of the solution contains 1.00 mole % ammonium sulfate. Take the heat capacity of the solution to be that of pure liquid water [4.184 kJ/(kg·°C)].

Answer 1

Reaction: 2NH_3(g)+H₂SO_4(aq)(NH₄)₂SO_4(aq)

Basis: 1 mol (NH₄)₂SO₄ is produced

a) Reference: Elements at 25⁰C

Obtain the heat of formation from Selected Physical Property Data.

Heat of formation of NH_3(g) is

Obtain specific heat data from Heat Capacities Table

For NH₃, the constants are a=35.15*10^-3, b=2.954*10^-5, c=0.4421*10^-8 and d=-6.686*10^-12.

Specific heat, C_p is

where T is the Temperature

Specific enthalpy of NH₃ is

where is Specific enthalpy

Substitute the values

Obtain the heat of formation from Selected Physical Property Data.

For H₂SO_4(aq),

Specific enthalpy of H₂SO₄ is

For (NH₄)₂SO_4(aq),

Specific enthalpy of (NH₄)₂SO₄ is

Energy balance is

where Q is the Heat withdrawn from the unit

n is the Number of moles of reactant or product

Thus the amount of heat withdrawn from the unit per mol of (NH₄)₂SO₄ produced is Q=-177 kJ/mol of (NH₄)₂SO₄ produced.

b) The product of the solution contains 1 mole% ammonium sulfate

1 mol% (NH₄)₂SO₄ solution= 1 mol (NH₄)₂SO₄*132 g/mol=132 g (NH₄)₂SO₄

where 132 g/mol is the Molar mass of ammonium sulfate

The solution will contain 99 mole of H₂O

  99 mol H₂O*18 g/mol=1782 g H₂O

Thus amount of solution is 1782+132=1914 g solution=1.914 kg solution

The heat withdrawn from the reactor is used to heat the product solution from 25⁰C to the final temperature.

Thus the final temperature, T_final is obtained as follows

where Q is the Heat required by the reactor. In this heat will be positive, as it is added to the reactor.

m is the Amount of solution

C_p is the Specific heat, C_p=4.184 kJ/kg⁰C

is the Change in temperature

Thus the final temperature is T_final=47.1⁰C