We combine Herschel observations of a total of 12 sources to construct the most uniform survey of HF and H _ { 2 } O in our Galactic disk .
Both molecules are detected in absorption along all sight lines .
The high spectral resolution of the Heterodyne Instrument for the Far-Infrared ( HIFI ) allows us to compare the HF and H _ { 2 } O distributions in 47 diffuse cloud components sampling the disk .
We find that the HF and H _ { 2 } O velocity distributions follow each other almost perfectly and establish that HF and H _ { 2 } O probe the same gas-phase volume .
Our observations corroborate theoretical predictions that HF is a sensitive tracer of H _ { 2 } in diffuse clouds , down to molecular fractions of only a few percent .
Using HF to trace H _ { 2 } in our sample , we find that the N ( H _ { 2 } O ) -to- N ( HF ) ratio shows a narrow distribution with a median value of 1.51 .
Our results further suggest that H _ { 2 } O might be used as a tracer of H _ { 2 } -within a factor 2.5- in the diffuse interstellar medium .
We show that the measured factor of \sim 2.5 variation around the median is driven by true local variations in the H _ { 2 } O abundance relative to H _ { 2 } throughout the disk .
The latter variability allows us to test our theoretical understanding of the chemistry of oxygen-bearing molecules in the diffuse gas .
We show that both gas-phase and grain-surface chemistry are required to reproduce our H _ { 2 } O observations .
This survey thus confirms that grain surface reactions can play a significant role in the chemistry occurring in the diffuse interstellar medium ( n _ { H } \leq 1000 cm ^ { -3 } ) .