# Kinetics

#### guthreb

Hi, I'm currently in Chem 104 in college and am working on kinetics. I am stuck on a couple problems and was wondering if some one could help me out.

Here's the first one:
The half-life for the radioactive C-14 is 5730 years. How long will it take for 25% of the C-14 atoms in a sample to decay? If a sample of C-14 initially contains 1.5 mmol of C-14, how many millimoles will be left after 2255 years?

Okay, so I think I figured the first part. Since the half life is 5730. Half of that would be 25% making it 2865 years. As for the second part, I'm not sure where to start. It does not give anything about whether it is zero, first or second order so I can't use an equation. Am I missing something? The other thought I had was to maybe just do unit conversion but that seems too easy for this problem. I think it has to involve the half-life expressions.

Lastly, there is another problem I am struggling with. It gives the equation: CHCl3 + Cl2 => CCl4 + HCl
It says: The reaction is first order in CHCl3 and one-half order in Cl2, Which of the following reaction mixtures would you expect to have the fastest initial rate?
3 Choices:
a. 3 CHCl3 molecules, 3 Cl2 molecules
b. 4 CHCl3 molecules, 2 Cl2 molecules
c. 2 CHCl3 molecules, 4 Cl2 molecules
I think it is b because 1st order reactions are faster than 1/2 order reactions- I think. However, the book and my professor has not talked much about 1/2 order reactions so that is what is confusing. I know if it was first and second order, it would be b for sure because second order would be fast but I'm not sure. Any help would be much appreciated!

Thank you!!

#### Unknown008

CHF Hall of Fame
1. a)
Not really. In 5730 years, 50% would have decayed. In 11460 years, 75% would have decayed.

This is not a linear pattern and you cannot say that in 2365 years, 25% would have decayed. Otherwise, after 5730+2365 = 8095 years, you would have 50%+25% decayed.

You need to use a formula here.

A = Ao (1/2)^(t/h)

A is amount left;
Ao is initial amount;
t is time elapsed;
h is half life.

A = 75% (when 25% decayed, 75% is left)
Ao = 100%
t = ?
h = 5730

75 = 100 (1/2)^(t/5730)

Solve for t.

b) Use the same equation. A = ?, Ao = 1.5 mmol, t = 2255 yrs, h = 5370 yrs.

2. I haven't heard of 1/2 order myself But I'd place my bet on b as well.