Final answer:
The powder that reacts with dilute hydrochloric acid to produce a gas that extinguishes a flame and does not support combustion is likely sodium carbonate (Na2CO3).
Step-by-step explanation:
When treated with dilute hydrochloric acid (HCl), certain metal carbonates release carbon dioxide (CO2) gas, which does not support combustion and will extinguish a flame.
The powder that reacts with dilute HCl to produce a gas that puts off a flame but does not itself burn is likely a carbonate. Among the given options, Na2CO3 (sodium carbonate) fits the description, as it will react with dilute HCl to form sodium chloride, water, and carbon dioxide:
Na2CO3(s) + 2HCl(aq) → 2NaCl(aq) + H2O(l) + CO2(g)
Since CO2 puts out flames and does not support combustion, the correct answer is (c) Na2CO3.