The isotopic abundance of naturally occurring hydrogen is as follows:
1H 99.985 atom %
2H 0.015 atom%
When H2 gas is formed from naturally occurring hydrogen, what percentages of the molecules have molecular weights of approximately 2, 3 and 4?
Compare to the tossing two coins.
P(Head ∩ Head) = P(Head) × P(Head) = 1/4
P(Head ∩ Tail) = 2 × P(Head) × P(Tail) = 1/2
P(Tail ∩ Tail) = P(Tail) × P(Tail) = 1/4
(Note that there are two ways to toss a head and a tail.)
The formation of hydrogen molecules from abundant hydrogen atoms is analogous, although there is a rather heavy bias against deuterium.
So:.....
P(1,1H2) = P(1H)×P(1H)
= 0.99985 × 99.985 %
=
P(1,2H2) = 2×P(1H)×P(2H)
= 2 × 0.99985 × 0.015 %
=
P(2,2H2) = P(2H)×P(2H)
= 0.00015 × 0.015 %
=
To determine the percentages of H2 molecules with molecular weights of approximately 2, 3, and 4, we need to consider the isotopic abundances mentioned:
1H: 99.985 atom% (mass = 1 amu)
2H: 0.015 atom% (mass = 2 amu)
H2 molecules can have three different combinations of isotopes:
1. Two atoms of 1H (1H2): mass = 2 amu
2. One atom of 1H and one atom of 2H (1H2H): mass = 3 amu
3. Two atoms of 2H (2H2): mass = 4 amu
To calculate the percentages, we'll use the isotopic abundances and the given molecular weights:
Percentage of 1H2 molecules:
= (Isotopic abundance of 1H * Isotopic abundance of 1H) * 100
= (99.985% * 99.985%) * 100
≈ 99.97%
Percentage of 1H2H molecules:
= (Isotopic abundance of 1H * Isotopic abundance of 2H) * 2 * 100
= (99.985% * 0.015%) * 2 * 100
≈ 0.03%
Percentage of 2H2 molecules:
= (Isotopic abundance of 2H * Isotopic abundance of 2H) * 100
= (0.015% * 0.015%) * 100
≈ 0.0000225%
Therefore, the approximate percentages of H2 molecules with molecular weights of 2, 3, and 4 are:
- 99.97% 1H2 (mass = 2 amu)
- 0.03% 1H2H (mass = 3 amu)
- 0.0000225% 2H2 (mass = 4 amu)
To determine the percentages of H2 gas molecules with molecular weights of approximately 2, 3, and 4, we need to consider the isotopes and their respective abundances.
1. First, let's look at the molecular weight of H2 gas. H2 consists of two hydrogen (H) atoms. The atomic weight of 1H is approximately 1, while the atomic weight of 2H, also known as deuterium, is approximately 2.
2. To find the molecular weight of H2 gas, we add the atomic weights of two hydrogen atoms: 1 + 1 = 2.
Now, let's determine the percentages of H2 gas molecules with molecular weights of approximately 2, 3, and 4.
Molecular weight 2: This represents normal hydrogen (1H) atoms combining to form H2 gas. The isotopic abundance of 1H is 99.985 atom %. Therefore, the percentage of H2 molecules with a molecular weight of approximately 2 would be approximately 99.985%.
Molecular weight 3: This represents a combination of one normal hydrogen atom (1H) and one deuterium atom (2H). The isotopic abundance of 1H is 99.985 atom %, and the isotopic abundance of 2H is 0.015 atom %. So, to calculate the percentage of H2 molecules with a molecular weight of approximately 3, we need to multiply the abundance of each isotope: 99.985% * 0.015% = 0.01499775%. This is a very small percentage.
Molecular weight 4: This represents two deuterium atoms (2H) combining to form H2 gas. The isotopic abundance of 2H is 0.015 atom %. Therefore, the percentage of H2 molecules with a molecular weight of approximately 4 would be approximately 0.015%.
In summary:
- Approximately 99.985% of H2 molecules have a molecular weight of 2.
- Approximately 0.01499775% of H2 molecules have a molecular weight of 3.
- Approximately 0.015% of H2 molecules have a molecular weight of 4.