help with excel solver

Most of the time when I get errors like that, I first check to make sure the spreadsheet is put together correctly and that the algorithm appears to converge correctly.

One observation, the formula for H appears to be using the group contributions for V instead of H.

Check what conditions cause the error and see if you should ever be near those conditions. For example, in this case, it appears that a divide by 0 is caused when all of the n(i)'s are 0 -- a 0 length polymer (which is a completely unreasonable condition, isn't it?). Perhaps a condition to specify a minimum polymer size, or a minimum number of methylene groups, or similar.

Another cause of errors is a poor choice of initial condition. As noted, a 0 length polymer is unreasonably, so using 0's (or anything near 0) for n(i) might be a poor choice for initial conditions.

n1 to n7 must be integers

Assuming the newer versions of Solver have the same options available in my older version, it should be real easy to set a condition that n1:n7 = int, though, at the same time, it might be just as easy to let Solver come to its best non-integer fit, then round the results to the nearest integer.

it returned a more reasonable solution but not the correct one

With this kind of problem (7 changeable variables) and the other complexities in this, I'm not at all surprised that there are multiple possible minima. How are you determining that the n1=2/n7=3 solution it converged on is not "the" solution?

Assuming you are using the default Newton/Raphson method, the way you deal with multiple solutions is to start with different initial guesses. I believe your version of Solver has an optional evolutionary algorithm that may do better at locating a global minima from within the many local minima that are present.