Specific heat capacity tells you how much energy is needed to raise the temperature of a given amount of material by 1 kelvin. That means the units must express energy per mass per temperature. The correct units are joules per unit mass per kelvin, i.e., J/(g·K) or J/(kg·K). Those show energy needed per gram (or per kilogram) for each degree of temperature rise. Other options don’t describe energy per mass per temperature. J/(mol·K) is molar heat capacity—per mole, not per unit mass. J is just energy, not tied to a temperature change per mass. J/K is heat capacity for a whole object (energy per one kelvin change for the entire body), not specific to mass.

Osmotic pressure in a dilute solution follows the van't Hoff relation, which mirrors ideal-gas behavior: the pressure needed to stop osmosis is proportional to the solute concentration and to temperature. The correct form is π = i M R T, where M is molarity, R is the gas constant, T is absolute temperature, and i is the van't Hoff factor that accounts for how many particles the solute produces in solution (i = 1 for non-electrolytes, greater than 1 when dissociation occurs, like NaCl giving two particles). This linear dependence on T and on the effective number of solute particles explains why osmotic pressure increases with temperature and with solute dissociation. Expressions that omit i miss the effect of dissociation, while those with T^2 or 1/T do not match the observed linear dependence on temperature.

The value of the equilibrium constant is determined by temperature, not by how much reactant you start with. At the same temperature, K is fixed for a given reaction. If you suddenly double the reactant concentration, the system shifts to re-establish equilibrium (Le Chatelier’s principle), producing more products or adjusting the mix until the ratio of products to reactants, each raised to their stoichiometric powers, matches the same K as before. So, once equilibrium is re-established, K remains unchanged. If the temperature were changed, then K would change accordingly; at constant temperature, it stays the same.

The mole concept: the amount of substance is quantified by counting particles, and one mole corresponds to 6.022 × 10^23 particles. So having exactly 6.022 × 10^23 particles means you have one mole of that substance. Mass and density describe how much material or how compact it is, but they do not specify the count of particles. Avogadro's number is the fixed count per mole (6.022 × 10^23), not the amount itself. Therefore, the unit that matches this description is the mole.