first-order process is the one whose rate is directly proportional to the concentration of drug undergoing reaction i.e. greater the concentration, faster the reaction.

**First-Order Kinetics (Linear Kinetics)**

If n = 1, equation 8.4 becomes:

dC/dt = -KC (8.10)

where K = first-order rate constant (in time^{–1}
or per hour)

From equation 8.10, it is clear that a **first-order process** *is the one whose rate is* *directly proportional to the concentration
of drug undergoing reaction i.e. greater the concentration, faster the reaction*.
It is because of such proportionality between rate of* *reaction and the concentration of drug that a first-order process
is said to follow **linear** **kinetics **(Fig. 8.3.).

**Fig. 8.3. ***Graph of first-order kinetics showing linear relationship between rate
of reaction and concentration of drug (equation 8.10).*

Rearrangement of equation 8.10 yields:

dC/C = -Kdt (8.11)

Integration of equation 8.11 gives:

ln C = ln C_{0} – Kt (8.12)

Equation 8.12 can also be written in exponential
form as:

C = C_{0} e^{- Kt }(8.13)

where e = natural (Naperian) log base.

Since equation 8.13 has only one exponent, the
first-order process is also called as **monoexponential
rate process**. Thus, a first-order process is characterized by** logarithmic **or** exponential kinetics **i.e.** ***a constant fraction of drug undergoes
reaction*** ***per unit time*.

Since ln = 2.303 log, equation 8.12 can be written as:

log C = log C_{0} - Kt/2.303 (8.14)

Or

log C = log C_{0} - 0.434 Kt (8.15)

A semilogarithmic plot of equation 8.14 yields a
straight line with slope = –K/2.303 and y-intercept = log C_{o} (Fig.
8.4.).

**Fig. 8.4. **

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