Problem 31 - Chemistry for Allied Health

Question

The concentration of product B increases from 0 to \(1.75 \mathrm{M}\) in 45 seconds. What is the rate of formation of \(\mathrm{B}\) ?

Step-by-Step Solution

Answer

The rate of formation of B is 0.0389 M/s.

Step 1: Understand the Concept of Rate of Reaction

The rate of formation of a product in a chemical reaction is defined as the change in concentration of the product with respect to time. This is usually expressed in moles per liter per second (M/s).

Step 2: Identify the Given Values

We are given that the concentration of product B increases from 0 to 1.75 M over a period of 45 seconds. This means C Bi= 0 M and C Bf= 1.75 M, and the time period t is 45 s.

Step 3: Calculate the Change in Concentration

The change in concentration of product B is calculated as the difference between the final and initial concentrations.\[\Delta [B] = [B_f] - [B_i] = 1.75 \, \text{M} - 0 \, \text{M} = 1.75 \, \text{M}\]

Step 4: Calculate the Rate of Formation

The rate of formation of product B is calculated using the formula:\[\text{Rate} = \frac{\Delta [B]}{\Delta t}\]Substituting the known values:\[\text{Rate} = \frac{1.75 \, \text{M}}{45 \, \text{s}} = 0.0389 \, \text{M/s}\]

Key Concepts

Concentration Change

In the context of a chemical reaction, concentration change is a measure of how the amount of a reactant or product in a solution evolves over time. This change is crucial for understanding the progress of a reaction. For any reaction, monitoring the change in concentration helps to:

• Determine the speed at which reactants are converted into products.
• Assess the efficiency of the reaction under various conditions.

In our example, the concentration of product B changed from 0 M to 1.75 M. This signifies that all the required reactants have gradually transformed into product B over the considered time span.
Calculating concentration change is the first step to finding out how fast the reaction occurs, which is often a measure of its effectiveness or feasibility.

Chemical Kinetics

Chemical kinetics is the field of chemistry that studies the rates of chemical reactions. It teaches us about the factors affecting reaction rates, such as concentration, temperature, and presence of a catalyst.
Understanding kinetics involves breaking down a reaction into simpler concepts:

• Reaction Rates: How quickly products are formed or reactants are consumed.
• Rate Laws: Equations that link the rate of reaction with the concentration of reactants.
• Factors Influencing Rates: Concentration changes, temperature, and catalyst presence impact how swiftly a reaction proceeds.

By studying these factors, chemists can tailor conditions to achieve efficient, desired reactions. In this exercise, by recognizing the time taken for a set concentration change, we delve into the core principles of chemical kinetics.

Reaction Rate Calculation

The reaction rate calculation gives insights into how fast a chemical reaction proceeds. It is typically expressed in terms of molarity per second (M/s), indicating the concentration change per unit time.
To calculate reaction rates, we use the formula:\[ \text{Rate} = \frac{\Delta [B]}{\Delta t} \]where \(\Delta [B]\) is the change in concentration, and \(\Delta t\) is the change in time.
This formula is vital in predicting how long it may take for a reaction to complete under given conditions. In the provided exercise, plugging in the values gave a reaction rate of 0.0389 M/s. This means that, in each second, the concentration of product B increased by 0.0389 M. Such calculations are fundamental because they help chemists design and control reaction conditions for optimal results, especially in industrial processes.