The sample of gas that is unreactive to flame tests and chemically reactive with limewater and bromothymol blue is Carbon dioxide.
Flame tests are performed to identify the unknown metals or metalloids. Upon burning on the flame, a compound gives characteristic colour, that helps in identification.
Carbon dioxide extinguishes the flame itself when placed upon it. And it is known to turn the lime water milky when reacts. Carbon dioxide also changes the colour of bromothymol blue. The change in colour is observed due to certain chemical changes like change in pH, formation of carbonic acid and conversion into more acidic form.
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