The half-life of tritium is approximately 12 years. What will be the molar ratio of tritium to helium-3 in a sealed sampel after 25 years?
k = 0.693/t1/2
Solve for k and substitute in the equation below.
ln(No/N) = kt
Solve for No/N
Then you want [N/(No-N)]. Check my thinking.
To determine the molar ratio of tritium to helium-3 in a sealed sample after 25 years, we need to understand the concept of half-life and use the knowledge of how tritium decays.
The half-life of tritium, as you mentioned, is approximately 12 years. This means that in 12 years, half of the tritium atoms in a sample will decay or transform into helium-3. After another 12 years (totaling 24 years), an additional half of the remaining tritium atoms will decay, leaving a quarter of the original tritium atoms. So, after 24 years, only 25% of the initial tritium atoms will remain, while the other 75% have decayed into helium-3.
Now, let's apply this understanding to the 25-year mark. Since one half-life is 12 years, we can determine the number of half-lives that have occurred in 25 years by dividing 25 by 12. This gives us approximately 2.08 half-lives.
Knowing that each half-life reduces the amount of tritium by half, we can calculate the remaining tritium as follows:
Remaining tritium = Initial tritium * (1/2)^(number of half-lives)
Since we want the molar ratio of tritium to helium-3, let's assume we have 1 mole of tritium initially. Thus, after 25 years, the remaining tritium would be:
Remaining tritium = 1 mole * (1/2)^(2.08)
Similarly, the helium-3 formed from the decay of tritium would be:
Helium-3 formed = 1 mole - Remaining tritium
Now, let's calculate the molar ratio of tritium to helium-3:
Molar ratio of tritium to helium-3 = Remaining tritium / Helium-3 formed
Using the calculations above, you can find the molar ratio of tritium to helium-3 in the sealed sample after 25 years.