A moon rock collected by a U.S. Apollo mission is estimated to be 3.70 billion years old by uranium/lead dating. Assuming that the rock did not contain any lead when it was formed, what is the current mass of 206Pb per 1.185 g of 238U in the rock? The half-life of 238U is t1/2 = 4.47 × 109 years.
How do I find t in the integrated rate law equation. I tried to fiqure this out for hours and im getting to pissed off and I already hate this class so please help.
I think t is 3.7E9 years according to the problem.
Here is what I would do.
k = 0.693/t1/2 and solve for k.
Then ln(No/N) = kt
You know k and t, solve for N/No.
If I understand the problem, the current mass U238 is 1.185g.
So you know No/N and N, solve for No which is the amount of U the sample started with. mass U238 initially - mass U today = mass U decayed and convert that to g Pb today.
mass Pb206 today = mass U decayed x (206/238) = ?
Thank god for dr bob
Thank you DrBob, you saved a couple hours of my life.
wtf dr bob
Ah, the joys of uranium/lead dating! Don't worry, I'm here to bring some laughter to your calculations.
To find the current mass of 206Pb per 1.185 g of 238U in the rock, we'll need to use the integrated rate law equation for radioactive decay. But fear not, I'll guide you through it with a smile.
The integrated rate law equation for radioactive decay is given by:
N(t) = N0 * e^(-λt)
Where:
- N(t) is the current amount of the isotope (in this case, 206Pb)
- N0 is the initial amount of the isotope (zero, since the rock didn't contain any lead when it formed)
- λ is the decay constant, which is related to the half-life (t1/2) by the equation λ = ln(2)/t1/2
- t is the time elapsed (in this case, the age of the rock)
Now let's get back to your question about finding t. Well, you're lucky I'm here, because I have a great solution for you: just ask the rock! Yes, that's right, ask the rock how old it is. I'm sure it'll have some hilarious tales to share!
But if you prefer a more conventional approach, you can rearrange the integrated rate law equation to solve for t. Take the natural logarithm of both sides:
ln(N(t) / N0) = -λ * t
Now substitute the values you have and solve for t. Just remember to use the decay constant (λ) calculated from the given half-life of 238U.
I hope my little detour brought a smile to your face. Don't forget to take breaks and keep a positive attitude. You got this!
To find the value of t in the integrated rate law equation, you need to use the equation specific to the order of the reaction.
For a first-order reaction, the integrated rate law equation is:
ln[A] = -kt + ln[A]₀
Where [A] represents the concentration of the reactant at time t, [A]₀ represents the initial concentration of the reactant, k is the rate constant, and t is the time.
In the case of a second-order reaction, the integrated rate law equation is:
1/[A] = kt + 1/[A]₀
Where [A] represents the concentration of the reactant at time t, [A]₀ represents the initial concentration of the reactant, k is the rate constant, and t is the time.
To find the value of t, you will need experimental data such as the concentration of the reactant at different time intervals. Plugging in the values of [A], [A]₀, and k into the respective integrated rate law equation, you can solve for t.
If you don't have experimental data and you simply need to understand the concept of finding t in the rate law equation, I recommend reviewing the lecture notes, textbook, or asking your professor for more clarification. It's important to understand the fundamental concepts and equations related to chemical kinetics to solve problems effectively.
Remember, it is normal to feel frustrated with complex concepts, especially in challenging classes. Take breaks, seek help when needed, and approach the problem with a calm mindset.