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Unfortunately, there is no way for the general public to determine load factors, much less how the seats are allocated.

There are two things you can find out. The first is a vague indication of how many seats remain available for sale. Again, only the airline itself will know the exact number, but there are several services that can tell you the minimum number of seats available to purchase. This will give you a vague idea of how empty or full a flight will be. The problem with this is that economy seats are broken down into a dozen or more fare classes, and the public services only tell you if a minimum of 9 seats are available in a particular fare class. These constantly shift around, so telling you that there are Y9 B6 M5 N3 available means that there are at least 9 seats available to purchase, not 23. In fact there may be only 7 seats available and the airline is betting that 2 people won't show up. And this information differs from point of sale, even for the same flight.

The other thing you can do is look at the seat map on the airline's website. But this only tells you which seats have been selected or assigned, not sold. I suspect you want to know this information before you buy the ticket, and at this point not many people may have selected seats.

In short, no, there is no way for you to know with any amount of confidence whether you'll have access to a row to yourself.