To produce 396 kg of ammonium sulfate, a minimum mass of 51 kg of ammonia is needed.
To calculate the minimum mass of ammonia needed to produce 396 kg of ammonium sulfate, we need to use the mole ratio from the balanced equation.
From the equation 2NH3 + H2SO4 -> (NH4)2SO4, the number of moles of ammonia is equivalent to the number of moles of ammonium sulfate produced.
Since the molar mass of ammonium sulfate is 132.14 g/mol, we can use the molar mass to convert the desired mass (396 kg) to moles:
396 kg * (1000 g/kg) / (132.14 g/mol) = 2995.2 mol
Therefore, the minimum mass of ammonia needed is also 2995.2 mol, which can be converted to kg using the molar mass of ammonia (17.03 g/mol):
2995.2 mol * (17.03 g/mol) / (1000 g/kg) = 51 kg