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They are written differently with zero order having moles first and second order having Liters first. Therefore, do they have different units so they must be written in this order or do they have the same regardless of the order?
The units of kr depend on the overall order of the reaction and ensure that kr x (concentration)a has the same units as the rate, namely, concentration/time. Thus, when the concentration is expressed in moles per liter and the rate is expressed in mol*L-1*s-1, the units of kr are a follows: 1st order = s-1. 2nd order = L*mol-1*s-1. 3rd order L2*mol-2*s-1.
Zero and second order k values have different units because of their relationship to the rate which is always mol/L/sec. So because rate = k for 0 order then the units are simply mol/l/s while Rate = k[A]^2 for a second order equation so the units for k will be L/mol/s to cancel out the mol^2/L^2 of the concentration.
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