Any time you replace an old faucet, you have to take off the locking nut that holds the faucet tight to the countertop. But often that nut will be frozen due to corrosion or mineral buildup from years of water seepage. Here are some nut-freeing tricks from Richard Trethewey. This Old House's plumbing and heating expert, listed in order from easiest to difficult.
1. Tighten the nut. Moving the nut in any direction is progress. Then try to loosen it using a correctly sized wrench.
2. Tap with a hammer. Jarring the nut can break its bond to the bolt. To make sure you hit the nut itself and not the surrounding threads, place a center punch on the nut and strike the punch with a hammer.
3. Apply heat. Metal expands slightly when hot, which may be enough to crack the nut free. You can do this with a hair dryer, heat gun, or propane torch. (If using an open flame within 12 inches of anything flammable, shield it with a flame-resistant fabric.) Try to turn the nut before it cools.
4. Soak the nut. If the bolt is covered with orange streaks or crumbly bits of rust, scrub them away with a wire brush and wipe the area dry. Then squirt a penetrating oil like Liquid Wrench on the threads as close to the problem as possible. Give it time to soak in. The longer you let the oil work, the better. If you have the time, try several applications over 24 hours. If the nut is encrusted with whitish lime deposits, remove what you can with a wire brush, then brush on white vinegar to dissolve what remains.
If a nut resists all these attempts to loosen it, it will have to be cut off with a hacksaw or reciprocating saw. Try making a vertical cut up through the threaded stem and nut, then crack the nut loose.