The half-life (t1/2) for a chemical reaction is the time it takes for the concentration of reactant to decrease to one-half its initial concentration. for a first-order reaction, the half-life is a constant at a given temperature. so the half-life is also the amount of time it takes for the concentration to change from one-half to one-fourth, and from one-fourth to one-eighth, etc. if the half-life for a first-order reaction is 12.0 minutes, what percentage of reactant remains unreacted after 48.0 minutes?

The percentage of reactant that remains unreacted is 6.25%

Explanation:

Let´s call [A]₀ the initial concentration of reactant A

In the first 12.0 minutes the concentration of A will drop to [A]₀/2

In 24.0 minutes the concentration of A will be reduced by half again

( [A]₀/2 / 2) = [A]₀ / 4

In 36.0 min the concentration of A will be ([A]₀/4 / 2) = [A]₀ / 8

And after 48.0 min the concentration of A will be ([A]₀/8 /2) = [A]₀/16

If [A]₀ is the 100%, [A]₀ / 16 will be (100 / 16) = 6.25%

Mathematically, you can express the concentration of A in this way:

[A] = [A]₀ / 2ⁿ

where:

[A] = concentration of A

[A]₀ = initial concentration of A

n =  t / t(1/2), where t = time and t(1/2) = half-life

In this case:

[A] = [A]₀ / 2^(48 min / 12 min)

[A] = [A]₀ / 2⁴

[A] = [A]₀ / 16

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

asthenosphere and convection