In general case, $($varying d$,$ T$,$ P$)$

p$0$v$0=$n$0$RT$0$

and

pv$=$nrt $($after reaction$)$

so

p$0/$RT$0=$C$0($Because C$0=$n$0/$V$0)$

p$/$RT$=$C

so$,$ C$/$C$0=$T$0$P$/$TP$0$ Isn't it$?$

What's wrong with my derive and why testbook derived In that way?