Adams County is a county located in the U.S. state of Washington. As of the 2010 census, the population was 18,728.The county seat is at Ritzville, and its largest city is Othello. The county was formed out of Whitman County on November 28, 1883 and is named for the second President of the United States, John Adams.Adams County comprises the Othello, WA Micropolitan Statistical Area, which is also included in the Moses Lake-Othello, WA Combined Statistical Area.he county was formed out of Whitman County on November 28, 1883 and is named for the second President of the United States, John Adams. Adams County comprises the Othello, WA Micropolitan Statistical Area, which is also included in the Moses Lake-Othello, WA Combined Statistical Area.