Rearranging to give y = mx + c

[Dave_]

The coverage of a physisorbed gas, q, is related to it’s pressure P in atmospheres and the equilibrium constant (hint) for adsorption K by the equation:

q = KP/(1 + KP)

Re-arrange the equation to give an equation of the form y = mx + c such that K can be obtained from the slope of a plot of y vs x, where x and y involve P and q, respectively.I wasn't 100% sure how to approach this question, I have so far rearranged the equation to give K:

K = q/P(1-q)

However I'm unsure on what to do next. Any help or pointers would be appreciated, Thanks!

 

[vela]

The problem didn't ask you to solve for K. It asked you to rewrite the equation in a form where you can identify K as the slope of a line. In the equation $y=mx+b$, $m$ is the slope, so you need to rearrange the original equation into the form (something) = K (something) + (constant). The first "something" should involve q, and the second one should depend on P.

It's also possible that you need to get it into the form (something) = (1/K) (something) + (constant). This time, you could find K by looking at the reciprocal of the slope of the line.

 

[epenguin]

Hard to reply without giving you answer, which vela almost has. Or answers as there are several, and several have in fact been commonly used. You just have to rearrange the equation you got such that you have a function of (P, q) on one side and another function of (P, q) on the other side and, a series of experimental pairs of values of P and q and hence your functions being known, the plot slope can tell you K.

Give us a couple of examples and we may tell you more.