Question

Help Attempting to derive the formula for ideal gas PV_m = kT is a constant, Sam ( a dedicated and curious student in P-chem class, who somethimes struggles with the understanding of class material) combined the laws of Boyle and Gay-Lussac in the following 6 step derivation:

1) PV_m = k₁,

2) V_m/T = k₂,

3) V_m = k₁/P ,

4) V_m = k₂T,

5) k₁/P=k₂T,

6) k₁/k₂=k=PT or PT=k

the conclusion in step (6) is obviously incorrect. what is the error? at which step(s) did the error(s) occur?

please rescue Sam by Showing the correct derivation.