For Whom Did Christ Die?

Jesus died for the "helpless" "ungodly" and "sinful." In Romans 5 Paul uses the pronouns "we" and "us" when describing who Christ died for. Does this mean His death paid for everyone? Or was the redemption more "particular." The doctrines of election and limited atonement are tied together; along with total depravity. Sinners are helpless unless God intervenes and saves them. He does this for some, but not for all. And He owes it to no one.