what is the molar concentration of human DNA in a human cell?

Excellent Excellent Question!

I think the molar concentration would depend on the total volume of your cell.

I don't measure cell volumes (no one does in your field, I suspect), as cell volume would surely vary depending of the cell type and function.  

[But let me know what your results are if you attempt this great feat].

In reference to recombinant DNA technology you can figure 12pg of dsDNA weight.  (Please double check my answer!).

But for experimental purposes, you should cut that in half...so you increase your chances of success by 50% if you are attempting to recombinate the whole genome.

Word of advice, especially in recomb DNA tech...

Generally speaking, you are looking to amplify a piece of the genome.  So you would want to think about the weight of that piece of genome.  Say 1kb, or something like that.

How many molecules of that 1kb genome are present in a collection of cells?  How many cells are there?

If you could isolate one cell, then you have 2 DNA sequences to work with.  How much do two sequences weigh?  Then multiply by the number of cells you have.  Viola!  You have the weight of molecules you can play with.

I like the way your thinking about this!

I share this information with you with hopes for peace within our Human race.  Use it peacefully for our Human race.

Best Karma to you!

Depends on what kind of cell - single or multi-nucleate - and the function of the cell. Some have lots more cytoplasm than others; and mature red blood cells have no nucleus...