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Chapter 7: Problem 19

If the concentration is expressed moles/litre, the unit of rate constant for a first-order reaction is (a) mole litre \(^{-1} \mathrm{~s}^{-1}\) (b) mole litre \(^{-1}\) (c) \(s^{-1}\) (d) \(\mathrm{mole}^{-1}\)

Short Answer

Expert verified
The unit of rate constant for a first-order reaction when the concentration is expressed in moles/litre is \(s^{-1}\), which corresponds to option (c).

Step by step solution

01

Understand the units of rate of reaction

The rate of a reaction is usually measured in terms of how fast the concentration of reactants decreases or the concentration of products increases. If the concentration is expressed in moles/litre and time is in seconds, then the units of rate of reaction is moles litre \(^{-1} \mathrm{~s}^{-1}\).
02

Apply the concept of order of reaction

In a first-order reaction, the rate of reaction is directly proportional to the concentration of a single reactant. The rate constant (k) is the proportionality constant. It's expressed mathematically as: rate = k [A], where [A] is the concentration of the reactant A. Rearranging the above equation to calculate the units of k gives: k = rate/[A].
03

Determine the unit of rate constant for a first-order reaction

Substitute the units for the rate of reaction and the concentration of the reactant into the equation for k: k = (moles litre \(^{-1} \mathrm{~s}^{-1}\))/(moles litre \(^{-1}\)). The mole litre \(^{-1}\) on both the numerator and the denominator cancels out, giving the unit for the rate constant of a first order reaction as \(s^{-1}\).

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Most popular questions from this chapter

For the chemical change \(A \rightarrow B\), it is found that the rate reaction doubles when the concentration is increased four times. The order in \(A\) for this reaction is (a) two (b) one (c) zero (d) half

The rate equation of a reaction is \(d x / d t=k[A]^{a}[B]^{b}\) for which the order of the reaction is (a) \(\mathrm{a}+b\) (b) \(a-b\) (c) a (d) \(b\)

On increasing temperature, rate of a reaction increases, because (a) the number of activated molecules increases (b) the number of activated molecules decreases (c) the number of activated molecules becomes zero (d) the activated molecules move with a low speed

In a first-order reaction, the conc. of reactant decreases from \(1.0 \mathrm{M}\) to \(0.25 \mathrm{M}\) in 20 minutes. The value of \(k\) is (a) \(0.6932\) (b) \(6.932\) (c) \(0.06932\) (d) none of these

The rate of a reaction, on increasing concentration of the reactants (a) increases (b) decreases (c) remains unaltered (d) none of these
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