Problem 32 - Chemistry for Allied Health

Question

The concentration of product B increases from \(0.50 \mathrm{M}\) to \(1.25 \mathrm{M}\) in \(2.5\) seconds. What is the rate of formation of \(\mathrm{B}\) ?

Step-by-Step Solution

Answer

The rate of formation of B is \(0.30 \text{ M/s}\).

Step 1: Understanding the Rate Formula

The rate of formation of a product in a reaction can be defined as the change in concentration of the product over a period of time. This can be mathematically expressed with the formula: \[ \text{Rate} = \frac{\Delta [B]}{\Delta t} \] where \( \Delta [B] \) is the change in concentration of product B, and \( \Delta t \) is the time interval over which the change occurs.

Step 2: Calculate Change in Concentration

Calculate the change in concentration \( \Delta [B] \) by subtracting the initial concentration of B from the final concentration of B: \[ \Delta [B] = [B]_\text{final} - [B]_\text{initial} = 1.25 \text{ M} - 0.50 \text{ M} = 0.75 \text{ M} \]

Step 3: Calculate Rate of Formation

Use the rate formula from Step 1, substituting the values for \( \Delta [B] \) and \( \Delta t \). Here, \( \Delta t = 2.5 \) seconds: \[ \text{Rate} = \frac{0.75 \text{ M}}{2.5 \text{ s}} = 0.30 \text{ M/s} \] This represents the rate of formation of B.

Key Concepts

Concentration Change

In chemical reactions, understanding the concept of concentration change is crucial to analyzing how a reaction progresses over time. Concentration refers to the amount of a substance in a given volume of solution, typically expressed in molarity (M), which is moles per liter.
Determining the change in concentration, denoted as \( \Delta [B] \), allows us to measure how much the concentration of product B has changed from the start to the end of the observation period.

• To find \( \Delta [B] \), subtract the initial concentration from the final concentration.
• For the exercise example, B's concentration increase from \(0.50 \text{ M}\) to \(1.25 \text{ M}\) results in a change of \( 0.75 \text{ M} \).

This difference tells us how much of B was formed over the allotted time, in this case, 2.5 seconds.

Rate of Formation

The rate of formation is a fundamental concept in chemical kinetics, describing how quickly a product is generated in a reaction. It's essentially the speed at which the concentration of a product increases.
For our exercise, this refers to how fast product B forms over time. Understanding this rate helps chemists to:

• Predict how a reaction proceeds.
• Adjust conditions to control the production of a desired product.

The rate of formation can be visualized as the slope of a graph plotting concentration versus time, which indicates how concentration changes at each moment in time. When calculated, these rates can help in comparing different reactions or conditions.

Rate Formula

The rate formula is a critical tool used to calculate the rate of formation of a product in a reaction. It is expressed as:\[ \text{Rate} = \frac{\Delta [B]}{\Delta t} \]where:

• \( \Delta [B] \) is the change in concentration of product B.
• \( \Delta t \) is the time interval over which this change occurs.

Applying this formula helps determine how fast or slow a reaction is occurring. Therefore, substituting the values from the exercise — a concentration change of \( 0.75 \text{ M} \) over \( 2.5 \text{ s} \) — into our rate formula gives:\[ \text{Rate} = \frac{0.75 \text{ M}}{2.5 \text{ s}} = 0.30 \text{ M/s} \]This calculation tells us that 0.30 moles of product B are formed per liter each second. Using the rate formula is invaluable for predicting and controlling reaction outcomes.