This is my area (more or less; I mostly work in structures but know a bit and some about propulsion) and I have to say that your question has few too many variables for a simple, explicit answer.
Backing up a bit, I[sub]sp[/sub] is known as specific impulse, or the ratio between the total impulse provided by the rocket to the mass of propellant burned. (For historical reasons and simplicity most industry planetary ballistics uses the total impulse divided by the surface weight of consumed propellant, giving a result in units of seconds, but the other definition is actually more correct.) Because the performance of a rocket will vary between full atmospheric pressure and vacuum (along with a few other parameters, particularly with solid fuel engines), the I[sub]sp[/sub] value stated in handbooks and promotional literature for orbital boosters is actually something of an average; propulsion gurus actually use thrust-time or impulse-time curves to predict payload capacity to a given orbit. Although specific impulse is widely used as a specific metric against which to compare different propellants in accomplishing the same goal (or as a general requirement for a mission of class such-and-such), for the question you are asking looking directly at the exhaust velocity, c is somewhat clearer.
For instance, assuming that we’re starting in vacuum from an Earth escape orbit, my back-of-envelope calculations say that you need any additional 2.9 km/s of velocity change to achieve a Hohmann (minimum energy) transfer. (There are other minimum energy transfers, but I don’t think that they require significantly less velocity change and their interval will be substantially longer). Once you get to Mars, you’ll need roughly 2.5 km/s of deceleration to circularize the orbit, giving a total delta velocity of about [symbol]D[/symbol]v=5.4 km/s. That delta velocity gives: [symbol]D[/symbol]v = c*[symbol]S[/symbol]ln(m[sub]i[/sub]/m[sub]f[/sub]) (the rocket equation)
Rearranging gives:c = [symbol]D[/symbol]v/ln(m[sub]i[/sub]/m[sub]f[/sub])
This gives you the exhaust velocity in terms of the overall mass fraction. (Of course, you are going to have to figure the return trajectory as well, but since we can assume that you’re going to leave a significant amount of your initial payload on the planet in terms of disposal lander components and fuel, equipment, et cetera, and only a modest amount of samples on the return journey, you’ll need to use a different payload mass for that leg.)
Now, if you want to convert that to I[sub]sp[/sub], then you’ll use the specific impulse equation, I[sub]sp[/sub]=c/gor alternatively, I[sub]sp[/sub]=c/(m[sub]i[/sub]-m[sub]f[/sub]) (which is, as alluded to above, more precise but less common in industry usage.)This gives an overall specific impulse requirement per mass difference, but doesn’t speak to total mass required. You can divide through by m[sub]f[/sub] to put the equation in terms of specific impulse per final mass in terms of exhaust velocity and mass fraction, but I find this a clunky and inelegant approach, especially since your mass fraction may change significantly with configuration.
If you are really interested in this topic, I recommend Prussing and Conway’s Orbital Mechanics (Chapter 5, pgs 85-87 has the relevant bits) as the clearest development of celestial mechanics I’ve found. Here is a decent page, too, albeit it throws it all at you at once.
Stranger