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");
Of course, using eval is dangerous unless you validate your input.
Update: Fixed code. * => +, ** => *
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