Problem 76 - Chemistry Matter and Change

Question

The concentration of Reactant A decreases from 0.400 \(\mathrm{mol} / \mathrm{L}\) at 0.00 \(\mathrm{min}\) to 0.384 \(\mathrm{mol} / \mathrm{L}\) at 4.00 \(\mathrm{min}\) . Calculate the average reaction rate during this time period. Express the rate in mol/(L. min).

Step-by-Step Solution

Answer

The average reaction rate during this time period is 0.004 mol/(L.min).

Step 1: Determine the change in concentration

To calculate the change in concentration, we'll subtract the final concentration from the initial concentration. Change in concentration = initial concentration - final concentration Change in concentration = 0.400 mol/L - 0.384 mol/L

Step 2: Determine the change in time

The question states the time period begins at 0.00 min and ends at 4.00 min, so the change in time is: Change in time = 4.00 min - 0.00 min = 4.00 min

Step 3: Calculate the average reaction rate

Now that we have both the change in concentration and the change in time, we can calculate the average reaction rate by dividing the change in the concentration by the change in time: Average reaction rate = Change in concentration / Change in time Average reaction rate = (0.400 mol/L - 0.384 mol/L) / 4.00 min Average reaction rate = 0.016 mol/L / 4.00 min Average reaction rate = 0.004 mol/(L.min) The average reaction rate during this time period is 0.004 mol/(L.min).

Key Concepts

Chemical Kinetics

The study of chemical kinetics is essential for understanding how reactions occur and at what pace. This branch of physical chemistry delves into the rate at which a chemical process proceeds as well as the steps and pathways through which the reaction takes place.

Factors such as temperature, concentration of reactants, and presence of catalysts can significantly influence these reaction rates. By analyzing the speed of these reactions, scientists and engineers can optimize processes, such as the manufacturing of chemicals, and understand phenomena like the degradation of pharmaceuticals or the metabolism of food in the body.

When chemical kinetics is applied to a real-world problem or an experiment, one typically begins by measuring changes in concentration of reactants or products over time, hence linking to the concept of reaction rates.

Reaction Rate Calculation

Reaction rate calculation involves quantifying the speed at which reactants are consumed or products are formed. It is expressed as the change in concentration of a reactant or product per unit time. Calculating the average reaction rate, as demonstrated in the exercise, requires the difference in concentration over a specific time interval.

To determine this average rate, a straightforward formula is used: \[\text{Average reaction rate} = \frac{\Delta [Reactant]}{\Delta \text{time}}\]where \(\Delta\) stands for 'change in'. Thus, the average reaction rate indicates how fast a reactant is disappearing or a product is appearing in the system. For some reactions, the average rate might not give a complete picture since reaction rates can vary throughout the process, but it provides an essential snapshot.

Molarity

Molarity, a key concept in chemistry and the backbone of reaction rate calculations, is a measure of concentration denoted as moles of solute per liter of solution (mol/L). Solute refers to the substance dissolved in the solution, which could be a solid, liquid, or gas.

In the context of the exercise, molarity indicates the concentration of Reactant A in the aqueous solution. It's a critical factor because reaction rates are often dependent on the concentration of the reactants. The higher the concentration, the more particle collisions occur, which increases the chance of reactions happening. Hence, understanding molarity is crucial when studying how reaction rates are influenced by changes in reactant concentrations.

Chemistry Time-Dependent Changes

Chemistry is a science that encompasses time-dependent changes, as chemical reactions can be fast or slow, and understanding these temporal elements is crucial. Over time, the concentration of reactants and products in a reaction mixture changes, providing insight into the reaction's dynamics.

By observing the rate at which reactants are consumed, as shown in the textbook exercise, we see how reaction rate calculations come into play to assess these time-dependent changes in the chemical systems. In the example, the decrease in the concentration of Reactant A over a four-minute period allows us to calculate the average reaction rate, giving a glimpse into the kinetics of the process. This understanding is vital for various applications, including the design of industrial reactors and pharmaceutical formulation.