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Question

Equilibrium constants is given (in atm) for the following reaction 0oC:
Na2HPO4.12H2O(s)Na2HPO4.7H2O(s)+5H2O(g);Kp=2.43×1013
The vapour pressure of water at 0oC is 4.56 torr
At what relative humidities will Na2HPO4.12H2O(s) be efflorescent when exposed to air at 0oC?

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Solution

Na2HPOH.12H2O(s)Na2HPO4.7H2O+5H2OKP=2.43×1013
KP=(PH2O)5
(PH2O)5=2.43×1013
pH2O=0.003atm
=2.28 torr
If vapour pressure with humidity is less than 2.28 torr then Na2HPO4.12H2O is efflourscent.
Relative humidity at limit =2.284.56×100=50%
Hence if relative humidity less than 50% Na2HPO4.12H2O is efflourscent.

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