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Because this is a relatively recent word, I can't find any etymological information in the sources I'm familiar with.
An old text that I found which uses this word is 《太平御覽·卷柏》: 氫鱍成性，終無自伸。 but I have no clue what this sentence has to do with hydrogen.
So my question is: why did people decide to pronounce hydrogen as qīng?
氫's pronunciation qīng comes from 輕.
According to this article, chemical elements were translated in more descriptive way in the 19th century, and hydrogen was named 轻气 (輕氣) "light gas". Later, the names were crippled to one character for each, so hydrogen became 轻 (輕). Finally, in 1919, every element was decided to be named systematically, where gases were unexceptionally covered by radical 气. Hence, hydrogen got its character 氫, and inherited 輕's pronunciation.
P.S.
Your quotation from 《太平御覽》 seems to be an digitalization bug. The original text reads: 屈巻成性終無自伸 "curled up by its nature, and never grows straightly". I doubt there's any occurrence of 氫 outside chemical literature.
