I was just offered a postdoc at 34 000 USD a year.
I am wondering whether this is an ok offer. Can someone give me feedback on this?
It sounds like it's on the low side for the sciences, but not unheard of. For comparison, NIH NRSA postdoc stipends start at about $39k for people with no previous postdoctoral experience and go up from there. Postdoc salaries can vary a lot by field, location, institution, etc.; if you have no other offers to compare with but want to know what's typical, I'd recommend searching online to find information that fits your background.
As Paul Garrett pointed out, you also need to consider the cost of living. According to CNN Money's cost of living calculator, $35k in Nashville is the equivalent of nearly $70k if you were living in Brooklyn. Of course these calculators are far from perfect, but they give you some indication of how prices and rents vary across the country. If you are going to live on $34k, Nashville is a good place to do it, and I would expect typical salaries there to be lower than in more expensive locations.
Ultimately, unless you believe there is discrimination or bias involved, I wouldn't worry too much about abstract notions of fairness, or even comparisons with other people in different circumstances. Instead, I would focus on three questions. What do you need to live happily in the short term? What are your long-term goals and prospects for achieving them? And what other options do you have, including not just similar postdoctoral offers but also career changes? Only you can weigh these considerations and decide whether a given offer is acceptable to you.
For what it's worth, most Ph.D. chemists that I've seen graduate and move to post-docs get around $40k. The amount depends on how much was budgeted in the grant proposal that is paying the post-doc salary and typically there isn't much wiggle room. Considering the dwindling grant resources, current hiring climate, and level of competition in this field, most are happy just to get a job.
On your question of fairness, did anyone else offer you another post-doc for more money? If not, I'd consider it fair.