In a broad 2011 rally that pushed the Dow up nearly a point in mid-morning trading Monday, Apple (AAPL) popped more than $7 (2.25%) to hit new record intraday highs — and to cross a major psychological barrier.

The company’s market capitalization — its stock price times the number of shares outstanding — is now more than $300 billion.

Apple has been the most valuable tech stock and the world’s second most valuable publicly traded company — after ExxonMobil (XOM) — since it passed Microsoft (MSFT) last May.

With oil prices running as high as they are, however, it won’t be easy to overtake the petrochemical giant. The gap between the two market caps had narrowed to less than $50 billion last October; now ExxonMobil’s lead has widened to more than $73 billion — despite Apple’s gains.

See chart below the fold.

Apple’s close Monday — at $329.57, up $7.01 (2.17%) — was an all-time record high.

[Follow Philip Elmer-DeWitt on Twitter @philiped]