Explain how to calculate the number of grams in 5.50 x 1022 atoms.
1 answer:
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A. The radioactive decay equation is N = N0
where T is the half-life (5730 years), N0 is the number of atoms at time t = 0 and N is the number at time t.
Rewriting this as:
(N/N0) =
Since N = (1/8) N0 and substituting known values:
1/8 =
Taking ln of both sides:
ln(1/8)= -ln(2)*t/5730
t = - 5730 * ln(1/8) / ln (2)
t = 17,190 years
The tree was cut down 17,190 years ago.
B. N0 = 1,500,000 carbon-14 atoms
Since N = (1/8) N0
N = 187,500 carbon atoms left
Explanation:
For the first part,
Reaction equation:
N₂ + 3H₂ → 2NH₃
Given:
Number of moles of NH₃ = 6 moles
Unknown:
Number of moles of N₂ = ?
Solution:
N₂ + 3H₂ → 2NH₃;
From the reaction above, we solve from the known specie to the unknown. Ensure that the equation is balanced;
2 moles of NH₃ is produced from 1 mole of N₂
6 moles of NH₃ will be produced from mole of N₂
= 3moles of N₂
The number of moles of N₂ is 3 moles
ii.
Given parameters:
Number of moles of sulfur = 2.4moles
Molar mass of sulfur = 32.07g/mol
Unknown:
Mass of sulfur = ?
Solution:
The number of moles of any substance can be found using the expression below;
Number of moles =
Mass of sulfur = number of moles of sulfur x molar mass
Insert the parameters and solve;
Mass of sulfur = 2.4 x 32.07 = 76.97g