Having Jake Peavy on the mound has helped the White Sox in recent outings, but the veteran right-hander hasn't fared well in his past couple matchups with the Royals.Peavy will try to end those struggles Tuesday night while seeking his third victory in as many starts.The White Sox (60-48) had split six games with the Royals in 2012 before a 4-2 victory in Monday's series opener. Gordon Beckham hit the tiebreaking solo homer during a two-run eighth and Kevin Youkilis added a run-scoring double, giving him five RBIs over his last three games.A.J. Pierzynski doubled home a run in the second inning before seeing his franchise record-tying five-game home run streak come to an end."We know what's on the line and where we want to go," said Beckham, who hadn't homered since June 20. "If we're going to get there, everybody's got to step up and pitch in."The victory kept Chicago 1 1/2 games ahead of surging Detroit in the AL Central, and the White Sox's performances against the Royals (45-63) could determine whether they capture their first division title since 2008.Chicago will play 11 more games against Kansas City, and Peavy (9-7, 3.04 ERA) will try to take advantage of one of those matchups while beating a team other than Minnesota.The right-hander has earned his past two wins against the Twins, allowing two runs in each game. He went eight innings and struck out eight in a 3-2 victory at Target Field on Wednesday."I feel excited to be able to help to this point, but we want to win," Peavy told the team's website. "It will be a satisfying season in this clubhouse for everybody, no matter what the numbers are at the end, if we find a way to win this (AL) Central and get in the playoffs."Peavy hasn't been nearly as effective in his past five games against the Royals, going 0-4 with a 5.97 ERA. He gave up six runs and a career-high 12 hits over seven innings of a 6-3 loss in Kansas City on July 14.In this start, the right-hander will pitch opposite a struggling Bruce Chen (7-9, 5.66), who is 0-3 with an 8.73 ERA over his last seven starts.The left-hander was pulled before the end of the third inning of his latest outing Thursday against Cleveland and was charged with four runs in a 7-6 victory."He might have thrown three pitches over 85 miles an hour," manager Ned Yost told the team's website. "Everything's soft and he's just not throwing the ball real well right now."He needs to pick his game up. To not be able to get out of the third inning, we need to do better than that."Chen gave up six runs over 4 2/3 innings to the White Sox at Kauffman Stadium on July 13 but did not get a decision in a 9-8 defeat.He might have better luck at U.S. Cellular Field, where he went 3-0 with a 0.90 ERA in three visits last season.