6. If concentrations measured in moles per liter, and time in seconds, what are the units of the rate constant for (a) a first order reaction, (b) a second-order reaction, and (c) a third-order reaction

The rate constant has units of

a) s⁻¹ or /s for a first order reaction.

b) /sM or (s⁻¹M⁻¹) or (L/s.mol) or (L.s⁻¹mol⁻¹) for a second order reaction.

c) /sM² or s⁻¹M⁻² or (L²/s.mol²) or (L².s⁻¹mol⁻²) for a third order reaction.

Explanation:

The rate of a chemical reaction is defined as the amount (in concentration terms) of reactant used up or products formed per unit time. It's units generally is given in the units of concentration per unit time.

Rate = M/s or written extensively as mol/L/s = mol/L.s

And for all types of orders of reactions, the rate of reaction is given as

Rate = kCⁿ

k = Reaction rate constant

C = concentration of specie involved in the reaction

where n is the order of reaction.

Note that the units of the rate of the reaction still has to be mol/L.s or M/s regardless of its order.

M = mol/L

a) For a first order reaction

Rate = kC

M/s = k × M

K = (1/s)

Hence, the rate constant has a unit of /s or s⁻¹

b) Second order reaction

Rate = kC²

M/s = k × M²

k = (1/Ms)

Units of /sM or s⁻¹M⁻¹ or (L/s.mol)

c) Third order reaction

Rate = kC³

M/s = k × M³

k = (1/sM²)

Units of /sM² or s⁻¹M⁻² or (L²/s.mol²)

Hope this Helps!!!