One way is to convert the string into Perl code:

my %atom_weights = (
   Pb => ...,
   C  => ...,
   O  => ...,
   ...
);

$_ = "Pb(CO3)2";

print("$_\n");

s/([0-9]+)/*$1/g;
s/([A-Z][a-z]*)/
   ($atom_weights{$1}
      or die("Bad element $1\n")
   ) . '+'
/eg;

s/\+(?=\*|$)//g;

print("$_\n");

print(eval($_), "\n");
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Of course, using eval is dangerous unless you validate your input.

Update: Fixed code. * => +, ** => *