Question
I have a tree that is full of pecans but leaves are falling and i have 1 or 2 limbs that have a black coating on it.

Answer
Hi Della,

I suspect that your pecan leaves may have an insect problem.  I suggest that you remove some of the leaves and see if the black coating can be removed.  If you can wipe it off with your fingers or fingernails, it suggests that the problem is sooty mold.  (If you should find that it does not come off, please let me know.)  Sooty mold grows on the leaves superficially.  It is not actually penetrating the leaves, but living on the surface.  The sooty mold itself will not hurt the plant directly, but it does block photosynthesis so the plant is less effective at making food from sunlight.  If you go the the link below and scroll to the bottom of the page, Figure 27 shows an image of sooty mold on leaves.
http://aces.nmsu.edu/pubs/_h/h-657/welcome.html

Where does the sooty mold come from?  Sooty mold lives on a sugary substance called honeydew that is produced by sap feeding insects.  These insects can cause damage if the populations are high.  They will suck the sap out of the leaves and can often cause the yellowing of leaves.  You can often see the insects, particularly on the underside of the leaves.  Aphids are the most common culprit.  The aphids that attack pecan leaves can be black, yellow or black and yellow.  Here is a link to an image of one of the aphids.
http://entoplp.okstate.edu/ddd/insects/blackmargaphid.htm

At this link, youc an get an idea of how small the aphids are in comparison to the pecan leaf.  Pretty tiny, so you may need a handlens or magnifying glass.
http://www.lsuagcenter.com/en/our_offices/research_stations/Pecan/Features/Pecan

Now, what should you do about aphids.  If you are finding 1 or more aphids per pinnately compound leaf, then you will want to treat for black aphids.  The threshold for other types of aphids is a little higher (several aphids per compound leaf), but since you are seeing sooty mold, treatment would be justified.  The image at the web link below shows you what a pinnately compound leaf is.  All the little leaflets make up one pinnately compound leaf.  So, if you find more than one aphid on the whole structure pictured, you should treat.  In the future, you will want to scout the trees and treat if you find aphids on the leaves.
http://botit.botany.wisc.edu/Resources/Botany/Morphology/Pinnately%20Compound%20

I would recommend treating your pecan tree with a systemic insecticide.  You should be able to find a product called Bayer Advanced Tree and Shrub Insect Control at your local garden center.  The active ingredient is imidacloprid.  You will want to follow the label directions to mix up the product.  Then, you will follow the directions to apply a drench to the root system.  This product will be taken up by the roots and carried up to the leaves.  I checked the label of the product and pecans are listed, but since formulations may vary between states, you will want to be sure that pecans are listed when you go to buy it in Texas.  They sell this product as both ready to use and as a concentrate, so be sure you have enough product to treat your tree.  If your tree is large, you will need more of the product to treat the entire canopy.

Good luck and let me know if you have any questions or problems.
--Jen