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

carbon is found in all living things. carbon atoms move constantly through

living organisms, the oceans, the atmosphere, and the earth’s crust in what is

known as the carbon cycle. the directions taken by carbon atoms through this

cycle are very complicated and can take millions of years to make a full circle.

all animals, from humans to the dinosaurs are part of the carbon cycle. when

animals eat food, they get carbon in the form of carbohydrates and proteins.

in animals, oxygen combines with food in the cells to produce energy for daily

activity and then gives off carbon. the carbon combines with oxygen to form

carbon dioxide (co2) and is released back into the atmosphere as a waste

product when animals breathe and exhale.

from 145-65 million years ago, earth was much

hotter than today and covered with dense,

tropical swamp forests. the trees and other

plants were immense and

provided an endless supply of

food for the giant animals that

roamed the land. somewhere in

the air above one of these

forests, a lone carbon atom has joined

up with two oxygen atoms to form a molecule of co2.

the co2 molecule was sucked into the tiny holes (stomata) on the leaf of a

fern plant and joined with sunlight, chlorophyll and water to make food and

energy in the plant’s cells through photosynthesis. the oxygen (o2) from the

co2 molecule was sent back into the atmosphere; the carbon atom (c) was

detached and used to make a molecule of sugar.

if that carbon atom had been eaten instead, a totally

different situation would have developed. let’s say

that a giant plant-eating dinosaur (herbivore) ate the

fern for breakfast, and swallowed the carbon in the

fern in the form of carbohydrates and proteins. in

the process of respiration, oxygen combined with

the carbohydrates and proteins in the dinosaur’s cells

to provide energy for its daily activity.  

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.