Problem 49 - Chemistry Matter and Change

Question

If a chemical reaction occurs at the rate of \(2.25 \times 10^{-2}\) moles per liter per second at 322 \(\mathrm{K}\) , what is the rate expressed in moles per liter per minute?

Step-by-Step Solution

Answer

1.35 moles per liter per minute.

Step 1: Identify the Given Rate

We are given that the rate of the chemical reaction is \(2.25 \times 10^{-2}\) moles per liter per second.

Step 2: Determine the Conversion Factor

To convert the rate from per second to per minute, we recognize that there are 60 seconds in a minute.

Step 3: Calculate the Rate Per Minute

Multiply the rate \(2.25 \times 10^{-2}\) moles per liter per second by 60 to convert it to moles per liter per minute: \[ 2.25 \times 10^{-2} \text{ mol/L/s} \times 60 \text{ s/min} = 1.35 \text{ mol/L/min} \]

Step 4: Conclusion

The rate of the chemical reaction at 322 K is \(1.35\) moles per liter per minute.

Key Concepts

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the speed or rate at which chemical reactions occur. It involves understanding how different conditions influence this rate and what mechanisms are involved in the reaction process. A reaction rate expresses how fast a reactant is consumed or a product is formed over time. This is a crucial aspect because it helps chemists control reactions in various applications, from industrial production to biological processes.

Factors influencing reaction rates include:

• Concentration of reactants: Higher concentrations generally lead to faster reactions.
• Temperature: Increased temperature usually increases the reaction rate.
• Presence of a catalyst: Catalysts speed up the reaction without being consumed.

In the context of our exercise, we are analyzing a specific reaction rate, given in moles per liter per second, and learning how to manipulate this rate for easier understanding and use.

Units Conversion

Unit conversion is an essential skill in science that allows us to express quantities in different ways. This is highly useful when trying to convey information in the most useful units for the problem at hand. In our exercise, the reaction rate is initially given in moles per liter per second (mol/L/s).

To convert this to moles per liter per minute (mol/L/min), we need to use a conversion factor. We know that 1 minute equals 60 seconds, so the conversion factor here is 60 seconds per minute. By multiplying the original rate by this factor, we convert the units properly:\[2.25 \times 10^{-2} \text{ mol/L/s} \times 60 \text{ s/min} = 1.35 \text{ mol/L/min}\]This multiplication effectively transforms the unit of time from seconds to minutes, providing a rate that is easier to interpret and possibly more relevant for longer time spans, particularly in practical laboratory or industrial settings.

Temperature Effects

Temperature strongly influences the rate of chemical reactions. Generally, as the temperature increases, so does the reaction rate. This is because temperature affects the kinetic energy of molecules. With higher temperatures, molecules move faster, increasing the frequency and energy of collisions required to overcome the activation energy of a reaction.

In the given exercise, the reaction rate is measured at 322 K. Although the conversion example does not change the temperature itself, understanding how temperature affects reaction rates is crucial. If a reaction's temperature were altered, its rate would likely change, aligning with the principles of the Arrhenius equation, which quantitatively describes the effect of temperature on rate constants:\[k = A \cdot e^{-E_a/RT}\]Where:

• \(k\) is the rate constant,
• \(A\) is the pre-exponential factor,
• \(E_a\) is the activation energy,
• \(R\) is the gas constant,
• \(T\) is the temperature in Kelvin.

Studying these effects empowers chemists to fine-tune reactions to achieve desired speeds and yields, which is particularly crucial in designing and optimizing industrial processes.