Hydrogen is the most abundant element in the universe constituting about 75 % of its elemental mass. — Physical Chemistry — Kinetics Chemistry Question
Hydrogen in outer space
Hydrogen is the most abundant element in the universe constituting about 75 % of its elemental mass. The rest is mostly helium with small amounts of other elements. Hydrogen is not only abundant. It is the building block of all other elements.
Hydrogen is abundant in stars such as the sun. Thus the Milky Way galaxy, consisting of over 100 billion stars, is rich in hydrogen. The distance between stars is several light years on the average. Hydrogen is also the major constituent of the interstellar space. There are about 100 billion galaxies in the universe. The empty space between galaxies is vast. For example, the Milky Way galaxy is separated from its nearest neighbor, the Andromeda galaxy, by 2 million light years. Hydrogen again is the primary constituent of the intergalactic space even though the number density is much less than in the interstellar space. The average density of matter in the intergalactic space, where the current temperature is the cosmic background energy of 2.7 K, is about 1 atom per m3.
Calculate the average speed, (8 RT / π M)1/2, of a hydrogen atom in the intergalactic space.
Model Answer
= 240 m s–1
Calculate the volume of a collision cylinder swept out by a hydrogen atom in one second by multiplying the cross–sectional area, πd2, by its speed where d is the diameter of a hydrogen atom (1×10–8 cm). Molecules whose centers are within the cylinder would undergo collision.
Model Answer
Volume of cylinder = (2)1/2 (3.14)(1.0×10–8 cm)2(2.4×104 cm s–1) = 1.1×10–11 cm3 s–1
Calculate the number of collisions per second experienced by a hydrogen atom by multiplying the above volume by the number density. How many years does it take for a hydrogen atom to meet another atom in the intergalactic space?
Model Answer
Collision / sec = (volume of cylinder) × (atoms / unit volume) =
= (1.1×10–11 cm3 s–1) × ( 1.0×10–6 cm–3) = 1.1×10–17 s–1
Time between collisions = 1 / 1.1×10–17 s–1 = 9×1016 s = about 3 billion years
Calculate the mean free path λ of hydrogen in the intergalactic space. λ is the average distance traveled by a particle between collisions.
Model Answer
(240 m s–1) × (9×1016 s) = 2.2×1019 m (about 2,000 light years)
Hydrogen atoms are relatively abundant in interstellar regions within a galaxy, there being about 1 atom per cm3. The estimated temperature is about 40 K.
Calculate the average speed of hydrogen atom in the interstellar space.
Model Answer
Speed is proportional to the square root of the temperature.
(240 m s–1) × (40 / 2.7)1/2 = 920 m s–1
Calculate the mean free path (λ) of hydrogen in the interstellar space.
Model Answer
Volume of cylinder =
= (2)1/2 × (3.14) × (1.0×10–8 cm)2 × (9.2×104 cm s–1) = 4.1×10–11 cm3 s–1
Collision / sec = (volume swept per second) × (atoms/unit volume)
= 4.1×10–11 cm3 s–1 × 1 cm–3 = 4.1×10–11 s–1
Time between collisions = 1 / 4.1×10–11 s–1 = 2.4×1010 s = about 800 years
Mean Free path = (920 m s–1)(2.4×1010 s) = 2.2×1013 m
λ(intergalactic space)/λ(interstellar space) = 2.2×1019 m / 2.2×1013 m = about a million
What do these results imply regarding the probability of chemical reactions in space?
Model Answer
very small