Feb 2013
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!!


CHF Hall of Fame
May 2010
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 :eek: But I'd place my bet on b as well.