When is it appropriate for a nation to become an imperialist power?

Expansion

Imperialism is defined as: Imperialism is an action where a country (usually an empire or kingdom) extends its power by acquisition of territories. It may also include the exploitation of those territories which is similar to colonialism which is generally regarded as an expression of imperialism.

Imperialism, much like any other sort of autocracy, is rooted primarily in servility. Imagine it this way (if it were a feudal society), there are barons (lowest), counts (second lowest), dukes (middle tier), grand-dukes (middle-high tier), kings (high tier), and finally emperors (god tier). In order for a person to be formally considered as an "emperor", a king must have sworn fealty towards you, or essentially you must possess multiple kingdoms under your rule.

Remember that of course there are empires that are merely in name (like the Empire of Trebizond).

2 Examples (Antique, and Modern)

Archaic (pre-colonization): Let's give the example of the Kingdom of France, let's say (hypothetical), that the French annex the Kingdom of Spain. Since the French monarch controls 2 kingdoms, it would essentially equate to an Empire

Modern: This is now also applying the old concept (obviously without the "feudal" model, but now there are simply actions that are considered "imperialistic". For example, acquiring a colony would be considered of imperialist demeanor, for example, Belgian Congo. Imperialist actions were also shown in for example, the U.S.A., when they made the Philippines a protectorate, overthrew the queen of Hawaii, made Haiti a protectorate, (essentially the "Big Stick" diplomacy). In the modern era, one can be imperialistic without being considered an "empire", this is why we don't refer Belgium, the U.S.A., or the Netherlands (despite them owning all of Indonesia) as empires, even though in technicality, they are.

0.32 mole

Explanation:

From the question given above, the following data were obtained:

Initial mole (n₁) = 0.31 mole

Initial pressure (P₁) = 742 torr

Final pressure (P₂) = 759 torr

Final mole (n₂) =?

The final mole of the gas in the drum can be obtained as follow:

P₁/n₁ = P₂/n₂

742 / 0.31 = 759 / n₂

Cross multiply

742 × n₂ = 0.31 × 759

742 × n₂ = 235.29

Divide both side by 742

n₂ = 235.29 / 742

n₂ = 0.32 mole

Thus, the final mole of the gas in the drum is 0.32 mole