use strict;
use warnings;
use Data::Dump qw/pp dd/;

local $/ = "";                           # $INPUT_RECORD_SEPARATOR to 
+split paragraphs °
my %res;                                 # result-set

while (my $block = <DATA>) {             # DATA as file-handle
    my (%f_num, $prefix);
    for my $line ( split /\n/, $block ) {
        my ($k,$v) = split /\s+/, $line; # key=value
        $f_num{$k} = $v                  # collect F<num>
          if $k =~ /^F\d+$/;
        $prefix    = $k                  # catch <solvent...> = 0
          if $k =~ /^solvent/ and $v == 0; # *
    }

    $res{"${prefix}_$_"} = $f_num{$_}    # copy with prefix 
      for keys %f_num; 
}

pp \%res;                                # display



__DATA__
F001            1.2
F101            3.2
solvent1      0
solvent2     3

F001            2.2
F101            7.2
solvent1      5
solvent2     0
[download]

{
  solvent1_F001 => 1.2,
  solvent1_F101 => 3.2,
  solvent2_F001 => 2.2,
  solvent2_F101 => 7.2,
}
[download]

update

*) added $k =~ /^solvent/ and to make it more fault tolerant.

an if-elsif-else chain would be even better to catch errors with unexpected data

°) changed from "\n\n" to match longer gaps too

update

Added comments. If you need further explanation, feel free to ask