What is the pH of the mitochondrial intermembrane space? The proton gradient is stored between the mitochondrial double membrane. More protons mean more hydronium ions and lower pH, but how much exactly?

I agree with @alina that it is well accepted that the pH difference across the inner membrane is ~0.5-1 units. However, the absolute value of the pH in the IMS will vary between organisms and even cells. It is experimentally difficult to measure it, therefore most of the times only the matrix pH has been reported. Using the output from the BioNumbers database as an example:

human endothelial cells ECV304: 6.88 (IMS), 7.78 (matrix)
human HeLa cells: 7.98 (matrix)
rat cardiomyocytes: 7.91 (matrix)