This is my hazy memory of a book I read about 20years ago:
A group of kids take a ride in a balloon (possibly at the behest of
Professor they know) whilst in the air they see the ground below
enveloped in a strange fog (an experiment of the professors that went
wrong?). When they land everyone on the planet has been turned to
stone.  Later they get involved in a fight with some criminals who
escaped the fog through working in a mine. The criminals kidnap the
girls in the group.

Hello.

Your book was "The Last Man Alive" by A.S. Neill.  The book was
originally published in 1938, and reprint editions date from the '60s
and '70s.

See this description from book dealers on Alibris:

"The adventures of a group who survived a poisonous cloud that turned
everyone else into stone."
http://www.alibris.com/search/search.cfm?qwork=3759951

Also available from dealers on Abebooks.com:
http://dogbert.abebooks.com/servlet/SearchResults?bx=off&sts=t&ds=30&bi=0&an=neill&tn=last+man+alive&sortby=2


There was also apparently a television version:

"The Last Man Alive
Based on A.S. Neill's best-selling novel of the same name, "The Last
Man Alive" is a delightful romp between fantasy and reality. Set in a
small and cozy boarding school nestled in the woods, the story begins
when a group of eight children gather around their favorite teacher,
Professor Birnenstiel. A colorful storyteller, Birnenstiel launches
into an incredible tale in which he and the children are the
protagonists. Their fantasy adventures take them into outer space,
from where they see a green cloud envelop the earth. Upon their
return, they discover that all human beings have been turned into
stone."
http://www.germanunited.com/en/programs/children/children06.html


It appears that someone has put the text of the book online, see:
A.S. Neill, "The Last Man Alive," Chapter 1
http://members.tripod.com/thelastmanalive/chapter_1.html

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search strategy:
google groups:
"turned * stone" balloon"
google:
"green cloud" "turned into stone"
"last man alive" neill

I hope this helps.

Quickly answered..great links.