In a 1 st order reaction, reactant concentration C varies with time t as :1C increases linearly with tlogC decreases linearly with tC decreases with 1tlogC decreases with 1t

In a first-order reaction, the concentration of the reactant (C) decreases exponentially with time (t). This is because the rate of reaction is directly proportional to the concentration of the reactant.

Mathematically, this can be expressed as:

Rate = k[C]

where k is the rate constant.

If we integrate this rate law, we get the equation:

ln[C] = -kt + ln[C0]

where [C0] is the initial concentration of the reactant.

This equation tells us that the natural logarithm of the concentration of the reactant decreases linearly with time.

So, the correct answer is: logC decreases linearly with t.

The other options are incorrect. The concentration of the reactant does not increase with time in a first-order reaction, it decreases. And the concentration of the reactant does not decrease with 1/t, it decreases exponentially with time. Similarly, the natural logarithm of the concentration of the reactant does not decrease with 1/t, it decreases linearly with time.