Work done by an expanding gas, how to solve this particular example? I just need help with one of these types of questions and I can handle the rest.  It is from a practice quiz on Coursera, Physical Chemistry.


  How much expansion work is done on the system when exactly 1 mol of solid ammonium chloride, $\ce{NH4Cl}$, decomposes completely
  to yield gaseous ammonia, $\ce{NH3}$, and hydrogen chloride, $\ce{HCl}$, at
  a temperature of 1280 K. Treat the expansion as
  irreversible and the gases formed as perfect.


I'm not sure how to compute the two volumes required to use the formula:

$$W = n R T \int\limits_{V_\mathrm i}^{V_\mathrm f}\frac{\mathrm dV}{V}$$

Do I assume $1\text{ atm} = 101.325 \text{ kPa}$.  I did that and was able to use the ideal gas law: $V = \frac{nRT}{P}$ to get the final volume of the 1 mole of gas, but I'm unsure how to choose the initial volume (0 won't work here as it leads to $-\infty$).


Is this the correct approach?  
If 1., then how do I also get the initial volume.  
If not 1., then how should I approach it?
You have system where 1 mole of solid (0 moles of gas) decomposes into two moles of gas at a constant temperature (given) and likely a constant pressure (not given). 

Your formula for work is not correct for this problem. You cannot have $n$ outside of the integral since $n$ is not constant. 

Let's write the total differential of the ideal gas equation:

$$\begin{align}
\mathrm{d}(PV)&amp;=\mathrm{d}(nRT) \\
P\mathrm{d}V + V\mathrm{d}P &amp;= nR\mathrm{d}T + RT\mathrm{d}n
\end{align}$$

Since $T$ is constant and $P$ is constant, we know $\mathrm{d}T=0$ and $\mathrm{d}P=0$, so this simplifies to:

$$P\mathrm{d}V = RT\mathrm{d}n$$

Can you do something with this relationship that avoids integrating with respect to (unknown) volumes?