NicholasW correctly states: No, is the short answer. You have to memorize them all.
The bopomo I mentioned above is the workaround. This syllabary is used in dictionaries. there is one more complicating factor and that is the matter of tones. Mandarin and Cantonese, the two major varieties of what we foreign devils loosely call Chinese, have four different tones that apply to any given syllable. I got the following off some web site at some time in the distant past:
Tones are usually described in terms of their beginning and ending points on a 5 point scale. Point 5 is the highest and 1 is the lowest.
Tone 1 in Mandarin is 55, since its beginning and ending points are the same - both at the highest end of the scale.
Tone 2 is a high rising tone. It begins at the middle of the scale (3) and rises to the highest point. We represent this as 35.
Tone 3 begins in the low mid range (2), drops to the lowest point (1) and then rises to level 4. We therefore use 214 to represent it.
Tone 4 begins at the highest point (5) and drops sharply to the lowest point (1). We therefore use 51 to represent it.
Sometimes you will see these tone numbers used in transcriptions of Chinese words, but more often you won't. I'm not sure how bopomo handles tones.
