In the rate equation

Rate = k [A]^x [B]^y

x and y indicate how sensitive the rate is to the change in concentration of A and B. Sum of these exponents, i.e., x + y gives the overall order of a reaction whereas x and y represent the order with respect to the reactants A and B respectively.

Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. Order of a reaction can be 0, 1, 2, 3 and even a fraction. A zero-order reaction means that the rate of reaction is independent of the concentration of reactants.

Another property of a reaction called molecularity helps in understanding its mechanism. The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction.

A first order reaction has rate constant 15 x 10^-3 s^-1. How long 5.0 g of reactant takes to reduce to 3.0 g?

34.07 s

The correct answer is option 1. 34.07 s.

To determine how long it takes for 5.0 g of reactant to reduce to 3.0 g in a first-order reaction, we need to use the integrated rate law for a first-order reaction:

\(\ln \left(\frac{[A]_0}{[A]}\right) = k t\)

Where:

\([A]_0\) is the initial concentration of the reactant.

\([A]\) is the final concentration of the reactant.

\(k\) is the rate constant.

\(t\) is the time.

Since we are working with masses, we can use them directly as proportional to concentrations. Hence:

\([A]_0 = 5.0 \text{ g}\)

\([A] = 3.0 \text{ g}\)

Rate constant, \(k = 15 \times 10^{-3} \text{ s}^{-1}\).

Rearrange the formula to solve for time \(t\):

\(t = \frac{1}{k} \ln \left(\frac{[A]_0}{[A]}\right)\)

\(t = \frac{1}{15 \times 10^{-3}} \ln \left(\frac{5.0}{3.0}\right)\)

\(t = \frac{1}{0.015} \ln \left(\frac{5.0}{3.0}\right)\)

\(t = 66.67 \times \ln (1.6667)\)

\(\ln (1.6667) \approx 0.5108\)

\(t = 66.67 \times 0.5108 \approx 34.07 \text{ s}\)

The time it takes for 5.0 g of reactant to reduce to 3.0 g is approximately: 34.07 s.