Question

The rate law is rate \(=k[\text { phenolphthalein }] .\) If the rate constant for the reaction is \(1.0 \times 10^{-2} \mathrm{s}^{-1}\) , what is the instantaneous rate of reaction when the concentration of phenolphthalein is 0.0025\(M\) ?

Short answer

The instantaneous rate of reaction when the concentration of phenolphthalein is 0.0025 M is \(2.5 \times 10^{-5}\text{ M}\cdot\mathrm{s}^{-1}\).

Step-by-step solution

Write down the given information

We are given: - Rate law: rate \(=k[\text { phenolphthalein }]\) - Rate constant, \(k = 1.0 \times 10^{-2} \mathrm{s}^{-1}\) - Concentration of phenolphthalein: \([\text { phenolphthalein }] = 0.0025\text{ M}\) We need to find the instantaneous rate of reaction when the concentration of phenolphthalein is 0.0025 M.

Substitute the given values into the rate law equation

We know the rate law and the values of \(k\) and \([\text { phenolphthalein }]\). Substitute these values into the rate law equation: rate \(= k [\text { phenolphthalein }]\) rate \(= (1.0 \times 10^{-2} \mathrm{s}^{-1})(0.0025\text{ M})\)

Calculate the instantaneous rate of reaction

Now, we can calculate the rate: rate \(= (1.0 \times 10^{-2} \mathrm{s}^{-1})(0.0025\text{ M}) = 2.5 \times 10^{-5}\text{ M}\cdot\mathrm{s}^{-1}\) The instantaneous rate of reaction when the concentration of phenolphthalein is 0.0025 M is \(2.5 \times 10^{-5}\text{ M}\cdot\mathrm{s}^{-1}\).

Key concepts

Instantaneous Rate

The instantaneous rate of a reaction provides critical insight into the speed of a chemical reaction at a specific moment. Consider it like checking the speedometer of a car; it tells you how fast the reaction is "going" at an exact point in time. To find the instantaneous rate, one needs to have the rate law for the reaction. The rate law is an equation expressing the rate of reaction in relation to the concentration of reactants and a rate constant, denoted usually by the symbol \( k \). By inserting the specific concentration of a reactant into this rate law, we are able to calculate the instantaneous rate. In our given problem, we did this by using \( k = 1.0 \times 10^{-2} \mathrm{s}^{-1} \) and a phenolphthalein concentration of 0.0025 M. The multiplication gave us the instantaneous rate of 2.5 \( \times 10^{-5} \text{ M}\cdot\mathrm{s}^{-1} \). Remember:

• Instantaneous rate is specific to a moment.
• Requires both rate constant and concentration for calculation.
• Expressed in units like \( \text{M}\cdot\mathrm{s}^{-1} \).

Reaction Kinetics

Reaction kinetics is a branch of chemistry that studies the speed or rate at which chemical reactions occur. It doesn't just tell us the rate, but also how we can alter the conditions to get the desired speed. Understanding the rate law is a vital part of kinetics, as it reveals how changes in concentration can influence the rate. Reaction kinetics is essential in both experimental and practical applications, such as designing industrial processes or controlling reactions in a laboratory setting. Factors influencing reaction rates include:

• Concentration of reactants: Higher concentrations typically lead to faster reactions.
• Temperature: Increasing temperature often accelerates reactions.
• Presence of catalysts: Catalysts speed up reactions without being consumed.
• Surface area: More exposed surface area can result in a faster reaction.

By manipulating these factors, chemists can control how quickly a reaction proceeds, making reaction kinetics a powerful tool in chemistry.

Concentration

In chemistry, concentration refers to the amount of a substance in a given volume and is usually expressed in molarity (M), which is moles per liter. Concentration is a pivotal variable in chemical reactions as it directly affects the reaction rate. For example, in our original exercise, the concentration of phenolphthalein modifies how fast it reacts in a given time frame when plugged into the rate law. Concentration is crucial because:

• It's a direct influencer of reaction speed: Higher concentrations increase the likelihood of reactant molecules colliding.
• Helps determine the extent of a reaction: Knowing the concentration allows chemists to predict how much product a reaction will produce.
• Essential for calculating equilibrium: In reversible reactions, concentration helps determine the position of equilibrium.

Always measure concentrations carefully, as they provide foundational information for understanding and predicting chemical reaction behaviors.