I treat athletic fields for ant often and I have been a certified commercial applicator for over 35 years.
When using baits at labeled rates, I suggest you apply with a 'shaker can'. You could take a quart jar and punch some holes in the lid and shake out the bait. For 14 acres, I would suggest you do this on an atv or utv.
You can spread a row about every 10 to 20 ft apart. Ants will travel about 30 feet to forage for food.
And, as someone suggested, treat when they are active. Put out a potato chip or a hot dog wiener and go check it in about 30 minutes. If there are ants on it, go ahead and treat. They are usually active in the morning and late afternoons. Not so much in the middle of the day, especially if it is really hot.
I think it would be very difficult to mix a bait with sand or anything else and get the rate right.
Another option would be to use some of the other products that are available besides baits. If you have some kind of spreader, there are products available that can be applied at 100 lbs per acre. It's much easier to apply 100 lbs per acre with a large spreader than trying to apply 1.5 lbs per acre with a large spreader.
Any product containing the active ingredient 'Bifenthrin' is very effective on ants and also will control many other insects, even mosquitoes. But, bifenthrin is a contact killer and has very little residual. In other word, it kills what it hits and then it's gone. And, for ants, it's best to apply bifenthrin just before a rain, so that the insecticide is carried down into the ground for a better kill.
Another product would be anything with the active ingredient 'Fipronil' This is very effective for fire ants, and last longer in the soil and will keep fire ants out for much longer. However, it is more expensive than bifenthrin and is very specific to only a few insects. It won't kill many bugs other than fire ants and a few others.
No matter what you do, always read and follow the label on any product you use.
The key to fire ant control is to treat as big of an area as you can. They will slowly move back into the treated area from the untreated areas.