Mathematics

Problem

In a laboratory experiment, the concentration

y

(mol/L) of a reactant and the temperature

x

(

^{\circ}

C) both vary with time. At

t=12\,

s the instruments show

\dfrac{dy}{dt}=-0.25\,\text{mol L}^{-1}\text{s}^{-1}

and

\dfrac{dx}{dt}=0.50\,^{\circ}\text{C s}^{-1}

. a. (i) Calculate the instantaneous rate at which the concentration changes with respect to temperature at

t=12\,

s. b. (ii) State the correct units of this rate. c. (iii) Determine whether the concentration is increasing or decreasing as temperature rises at this instant.

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