Suppose I have a molar concentration $[C]$ in $mol/m^3$ in a continuous reactor, from which the differential equation is as follows:

$ \frac{\partial [C]}{\partial t} = k[A][B] + \phi C_{,in} - \phi C_{,out}$

Where the first term is the rate law with rate constant $k$, and with concentrations of reactants $A$ and $B$, as $A+B \longrightarrow C$.

The second and third terms are inflows and outflows of substance $C$ in a continuous reactor.

The outflow of $C$ is measured, and therefore I need to have each term correlate with each other by having the correct dimensions. I have the following question:

Suppose $C$ is a gaseous substance, and the measured output is in $vol\%$ (volume percentage), how would I convert $\phi C_{,out}$ or $\phi C_{,in}$, which is in $[Nm^3/s]$ (normal cubic meter per second), to $vol\%C$? I found the following:

$\hspace{30pt} \phi_{C_{,out}} = \dfrac{p\dfrac{vol\% C}{100\%}}{RT}\phi_{out}\hspace{10pt}$ but this leads to a wrong dimension $[m^3/mol]$ for the $vol\%$