What is the value of an 1841 gold US 1 dollar coin?

The US didn't start minting gold dollars until 1849. Please check again and post a new question.

If the coin is about the size of a quarter and has a picture of the Statue of Liberty on the back, it's not gold and not from 1841.* You have one of the modern presidential dollar coins that have been issued since 2007. It's brass, not gold, and is only worth $1. 1841 is the year that W. H. Harrison served as president. The minting date is on the coin's edge. You should be able to get lots of them from any major bank at $1 each, so feel free to spend it.

(*) The Statue of Liberty was built in 1886 so it couldn't exactly be on a coin from 1841 unless it was minted by a time traveller ...