Do all the molecules in 1 mol sample of oxygen gas have the same energy at 273 k?

If it is assumed that it is an ideal gas, then all of the molecules would have the same energy. Ideal gases are known to have "elastic collisions". This means that no energy is lost, gained, or transferred through collisions. If the gas is a real gas, then molecules within the contained oxygen would have different energy. Each molecule would have different velocities of how fast they are moving through a volume and collisions between one another would result in a transfer of energy between molecules.

answer : one can design an experiment using a liquid and an additive that can be added to the liquid and observe the chemical changes in the reaction species.

one would need a beaker which is filled with a known amount of the liquid in which thermometer is placed to measure the temperature changes; after addition of the additive to the liquid solution one can note down the temperature change and find whether the reaction is endothermic or exothermic in nature. by subtracting the initial temperature value with the final temperature one can find the temperature changes.

various combinations of liquid and additive can be used. liquid in this case can be a known quantity of water and additives can be epsom salt or without epsom salt the experiment can be conducted to notice the changes. water and ice, hydrogen peroxide and dry yeast, vinegar and baking soda,etc.