If you want figures...there IS an equation which does this for you.
Given an electrode potential E cell (i.e. reduction potential of cathode minus reduction potential of anode) at standard conditions
Your actual electrode potential is given by:
E cell = E cell standard - RT/nF * ln Q
R is the ideal gas constant
T is the temperature in Kelvin
n is the number of moles of electrons transferred per mole of reaction (so for instance, in Cu + F2 => CuF2, there are two electrons transferred per mole of reaction so n=2 for that reaction)
Q is the reaction quotient, or concentration fraction. Except you don't use concentrations for gases; you use the partial pressure of the gas in bars (atm or bars aka 100 kPa, depending on which convention you follow). Note that at standard states, when the pressures and concentrations are equal to 1 M or atm, Q=1, so ln Q = 0. As expected.
ln is the natural logarithm
So, if you have a LOT of chloride ion and not much chlorine gas, the reaction quotient will be very small, much smaller than 1. The natural log of this is hence negative, and the -RT/nF term becomes positive. You have an increase in cell potential which may be larger than the cell potential of the oxidation of water.