142 ATOMS, IONS, SALTS, AND SURFACES 



If the increase of volume (A v) is infinitesimal, it is designated by dv, so 



dW=p-dv. (3) 



But by the gas law 



P —, (4) 



so 



dW=NRT - . (S) 



The work (W) done by the reversible expansion of the gas from a volume to a 

 volume V2 is 



W= I 'dW = NRT\ '^ = NRTln^. (6) 



Since, however, the volume of a perfect gas varies inversely as its pressure (/>), 



W = NRTln^. (7) 



P2 



Consider a chemical reaction 



aA+bB%eE+fF , 



in which all of the substances are in the gaseous state. Let the initial pressures of the 

 gases A and B be p^ and p^ and the final pressures of E and F be p^ and /?/. Assume 

 that a large box contains all of these four gases in equilibrium with one another at 

 pressures pA, pB, pE, and pp- Let the gases A and B at pressures p^ and p'g be con- 

 tained in two cylinders provided with pistons. 



The first step in the process is to change the pressure /?j to pA- The work done by 

 a gas in such a process equals the number of mols (c) of gas times RT times the loga- 

 rithm of the initial pressure divided by the final pressure, or 



P'a 



W, = aRTln^. (8) 



Pa 



By the use of a well-known characteristic of logarithms, this becomes 



W. = RTln^. (9) 



Pa 



The similar equation for the gas B is 



W2=RTln^. (10) 



Pb 



The gases A and B are now at pressures equal to their partial pressures in the 

 large equilibrium box. Suppose that the cylinders which contain these gases are set on 



I 



