If we have h2o d2o d stands for deuterium and na how would, Chemistry

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If we have h2o d2o d stands for deuterium and na how would

If we have H2O, D2O (D stands for deuterium), and Na, how would we react these to form HD pure gas?

The answer was:

Na + H2O --> NaOH + (1/2) H2

Na + (1/2)H2 --> NaH

NaH + D2O --> HD + NaOD

How is this the answer? How would we know which compounds to react and such?

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