Perhaps helpful or not to you, this was my general thought process:
1. I started by writing "while(){" without filling in cndx yet.
2. I saw that you had blank line separated records.
So, I just coded a line to get that record and coded the subroutine.
There are many ways to write this sub, I just picked an obvious one
3. Then I applied your rules to get the solvent name from that record.
4. Then I wrote loop to iterate over F values
5. then I decided to end on eof and filled in while cndx with an eof check.

So, that is how I got to draft #1. Now I see that I could move getting the record into the while condx and stop going on a null hash. All sorts of improvements could be made. I wanted to demo iterating over the keys of the record and getting a subset of matching keys with grep. This is not perfect code, but I hope easy for you to understand.

use strict;
use warnings;
use Data::Dumper;

my %results;   #pick a better name for this!!

my $eof_seen = 0;
while (!$eof_seen)
{
   
   my %record = get_record();
   
   my ($solvent) = grep {/^solvent/ and $record{$_}==0}keys %record;
   
   foreach my $F (grep {/^F/}keys %record)
   {
      $results{$solvent."_".$F}= $record{$F};
   }
   
   $eof_seen=1 if (eof(DATA));
}
print Dumper \%results;


sub get_record  #blank line separated records
{
   my %record;
   my $line;
   
   while (defined ($line = <DATA>) and $line !~ /^\s*$/)
   {
       my ($key, $value) = split ' ',$line;
       $record{$key} = $value;
   }
   
   return %record;
}

=Prints
$VAR1 = {
          'solvent1_F101' => '3.2',
          'solvent1_F001' => '1.2',
          'solvent2_F101' => '7.2',
          'solvent2_F001' => '2.2'
        };
=cut

   

__DATA__
F001            1.2
F101            3.2
solvent1      0
solvent2     3

F001            2.2
F101            7.2
solvent1      5
solvent2     0
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