You should always look up pronunciations in a dictionary to be sure, because no rules on this subject are accurate 100% of the time.
In general, the rules for pronouncing vowels are strongly linked to the position of stress in a word in English (which unfortunately is not written). All English words with more than one syllable have a syllable with "primary stress" (usually marked with a raised line before the syllable in phonemic transcriptions) and may have other syllables with "secondary stress" (usually marked with a lowered line before the syllable).
Knowing about secondary stress is useful in this case because of the following three facts:
- In general, the vowel /ə/ cannot occur in syllables with any kind of stress (primary or secondary).
- Pretty much all words in English have either a primary stress or a secondary stress on one of the first two syllables.
- Secondary stress often appears on syllables that are two syllables away from the primary stressed syllable.
The words "apprehend" and "application" both have secondary stress on the first syllable. We can transcribe their pronunciations like this:
In "approve, appraisal, appreciation," the first syllable comes directly before a stressed syllable, so it doesn't receive any secondary stress. We can transcribe the pronunciations of these words like this: /əˈpruːv/, /əˈpreɪzl̩/, /əˌpriːʃiˈeɪʃn̩/.
Sometimes you can use the way a word ends to figure out where the stress is: e.g. words ending in -ation have primary stress on the syllable that contains the "long a" sound /eɪ/ and comes right before the -tion part. Counting back from that, you can figure out that application probably has secondary stress on the first, rather than the second, syllable.