Gate radical wrapping from above, the indexing component and a contracted form of 門. It pictures a double-leaf gate, and in 阔 it sets the visual stage — a wide-open gateway. Same wrapper sits in 间 between, 闷 stuffy, 闹 noisy, 闯 dash through.
Inside the gate sits 活 huó, supplying the sound with a regular shift huó → kuò (an old h/k alternation). The 活 itself shows water (氵) + tongue (舌), picturing living motion. Inside the gate: 'wide-open space where life flows' — fits 'broad, vast'.
