Question

\(2 \mathrm{P}+3 \mathrm{Q}+\mathrm{R} \rightarrow\) product If for this reaction Rate \((\mathrm{R})=\mathrm{K}[\mathrm{P}]^{-1 / 2}[\mathrm{Q}]^{1}[\mathrm{R}]^{1 / 2}\) The order of this reaction is a. Zero b. Ist c. IInd d. \(3 / 2\)

Short answer

The reaction is first order, option b.

Step-by-step solution

Identify Reaction Rate Expression

The rate of the reaction is given by \( R = K[P]^{-1/2}[Q]^{1}[R]^{1/2} \). This expression shows the dependence of the rate on the concentration of each reactant.

Determine the Partial Orders

To find the order with respect to each reactant, we look at the exponents in the rate expression: - Order with respect to \( P \) is \(-1/2\).- Order with respect to \( Q \) is \( 1 \).- Order with respect to \( R \) is \( 1/2 \).

Sum the Partial Orders

The total order of the reaction is the sum of the individual orders. Calculate:\[ -\frac{1}{2} + 1 + \frac{1}{2} = 1 \]

Conclusion

The sum of the orders indicates that the overall order of the reaction is 1. Thus, the order of this reaction is first order.

Key concepts

Understanding Reaction Rate

The reaction rate is a vital aspect of chemical kinetics. It tells us how fast or slow a reaction proceeds by measuring the change in concentration of reactants or products over time. If you picture a chemical reaction like a race, the reaction rate would be how quickly the participants (reactants) transform into winners (products).

Factors that influence reaction rates include:

• Concentration of reactants: More molecules can collide if they are in a higher concentration, leading to faster reactions.
• Temperature: Higher temperatures provide molecules with more energy to collide successfully.
• Presence of a catalyst: Catalysts lower the energy barrier, increasing reaction speed without being consumed.

Understanding reaction rates helps chemists to control conditions, optimizing reaction efficiency in various applications ranging from industrial manufacturing to biological processes in living organisms.

Grasping Partial Order in Reactions

Each reactant in a chemical reaction has a partial order. This is the power to which its concentration is raised in the rate expression. Essentially, it explains how a reactant's concentration affects the reaction rate.

For example, consider the reaction \[2 \mathrm{P}+3 \mathrm{Q}+\mathrm{R} \rightarrow \text{product}. \] In the rate expression \[R = K[P]^{-1/2}[Q]^{1}[R]^{1/2},\] the partial order with respect to

• \([P]\) is \(-1/2\),
• \([Q]\) is \(1\), and
• \([R]\) is \(1/2\).

These partial orders inform us about each reactant's contribution to the overall rate. Notably, a negative partial order indicates an inhibitory effect on reaction rate, while positive suggests enhancement. Recognizing these individual effects is crucial for accurately modeling and optimizing reactions.

The Role of the Rate Expression

A rate expression is a mathematical equation that links the rate of a reaction to the concentration of its reactants, often including a constant known as the rate constant (\( K \)). It's a powerful tool in understanding the dynamics of a reaction.
In the example \[ R = K[P]^{-1/2}[Q]^{1}[R]^{1/2}, \] the rate expression dictates how changes in concentrations of \( P \), \( Q \), and \( R \) influence the reaction speed. This expression contains information derived from experimental data and is specific to a given reaction under defined conditions.

• \( K \) is specific to temperature and other conditions; it remains constant unless these conditions change.
• The exponents, or partial orders, show the sensitivity of the rate to each reactant's concentration.

To analyze a reaction thoroughly, understanding the rate expression is essential. It not only aids in predicting reaction behavior but also assists in designing conditions to achieve desired reaction rates in practical scenarios.