Does the term 'silver nitrate' express all of its constituent chemical elements? My professor gave my class a set of practice questions for the mid-term. One of those questions asks for the molar mass of a number of chemicals, such as lithium bromide and silver nitrate. We haven't studied those chemicals, so there's little reason for the professor to expect us to have memorized the elements that constitute those chemicals. In the case of lithium bromide, the term informs us of its constitution. Whereas,'silver nitrate' informs us that the chemical $ \mathrm{AgNO_3}$, includes silver and nitrogen, but I don't see anything in the term that would inform the reader that the chemical includes $ \mathrm{O_3}$.

Is there anything in the term 'silver nitrate' that would inform a reader that the chemical includes $ \mathrm{O_3}$? 

More generally, is there a set of rules that relates the chemical constituents of chemical substances to the linguistic constituents of the terms that designate them?
You should know that nitrate is a polyatomic ion with the molecular formula $\ce{NO3^-}$. For example:

Sulfate is a polyatomic ion with the molecular formula $\ce{SO4^{2-}}$;
Sulfite is a polyatomic ion with the molecular formula $\ce{SO3^{2-}}$;

Nitrate is a polyatomic ion with the molecular formula $\ce{NO3^-}$;
 Nitrite is a polyatomic ion with the molecular formula $\ce{NO2^{-}}$

At first glance, the nomenclature of the polyatomic negative ions seems difficult. 
When the name of the ion  ends in either -ite or -ate:


The -ite ending indicates a low oxidation state.
The -ate ending indicates a high oxidation state.


I agree with you that at the beginning, it seems difficult. But by practicing, you find this quite easy.