what is the answer?

Question

I.                  Mono-ammonium phosphate (NH₄H₂PO₄), a fertilizer, can be prepared by the action of sulfuric acid on a mixture of calcium phosphate and ammonium sulfate.  It should be noted that calcium sulfate is formed as a by-product. Write the balanced chemical equation for the reaction.

a.      Given a 95% yield for the reaction, determine the cost of raw materials (in $/kg) for producing the fertilizer. The individual costs for the raw materials are as follows: sulfuric acid ($200/1000 kg), calcium phosphate ($300/1000 kg), and ammonium sulfate ($375/ 1000 kg).

b.     Diammonium phosphate ((NH₄)₂HPO₄) can be produced by reacting mono-ammonium phosphate with ammonia. If this reaction has a 90% yield, how many kg of ammonium sulfate are required to produce 1000 kg of diammonium phosphate?

c.      Compare the nitrogen and phosphorous content of both mono-ammonium phosphate and diammonium phosphate. 

Answer 1

Ca3(PO4)3 + (NH4)2SO4 + 2 H2SO4 = 2 NH4H2PO4 + 3 CaSO4

a) According to the reaction if we take 310kg of CaSO4, 132 kg of (NH4)2SO4 and 2*98=196 kg H2SO4, we will have 230 kg of fertilizer. Giving that yeald is only 95% the actual amount will be 218.5 kg.

Total cost for that will be: $300*0.310 + $375 * 0.132 + $200 * 196 = $181.7 (per 218.5 kg), or $181.7*1000/218.5 = $831.58/1000kg

b) For 100% yeald 1000*132g/mol / 115g/mol = 1147.82 kg

For 90% yeald we will have 1147.82*0.9=1033 kg

c) In NH4H2PO4 N content will be 14/115=0.1217 or 12.17%; P content 31/115 = 0.2696 or 26.96%

In (NH4)2HPO4 N content is 2*14/132 = 0.2121 or 21.21%, P content is 31/132=0.2348 or 23.48%