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K values will not have units because they are "active" or "activities." Page 400 in the 7th Edition explains how activities are pure numbers and are unit less. More importantly, if you solve for K, you have (mol/L) / (mol/L), which cancel out leaving no units. So Kc and Kp will always be unit less, but you must ensure that when calculating for Kc and Kp the units are correct!
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