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?

Short answer

The rate of the chemical reaction in moles per liter per minute is \(2.25 \times 10^{-3}\ \text{moles/liter/minute}\).

Step-by-step solution

Identify the given rate

The given rate of the chemical reaction is \(2.25 \times 10^{-2}\) moles per liter per second at 322 K.

Convert seconds to minutes

In order to convert the rate from moles per liter per second to moles per liter per minute, we need to use a conversion factor for time. We know that 1 minute is equal to 60 seconds, so the conversion factor we will use is: \(\frac{1\ \text{minute}}{60\ \text{seconds}}\)

Multiply the given rate by the conversion factor

Now, multiply the given rate by the conversion factor to change the units of the rate expression: \((2.25 \times 10^{-2}\ \text{moles/liter/second}) \times \frac{1\ \text{minute}}{60\ \text{seconds}}\)

Simplify the expression

Cancel out the units of seconds in the expression and simplify: \((2.25 \times 10^{-2}\ \text{moles/liter}) \times \frac{1\ \text{minute}}{60}\) \(= 2.25 \times 10^{-2} \times 1 \times 10^{-1} \ \text{moles/liter/minute}\)

Calculate the rate in moles per liter per minute

Finally, calculate the rate in moles per liter per minute: \((2.25 \times 10^{-2}) \times (1 \times 10^{-1}) \ \text{moles/liter/minute}\) \(= 2.25 \times 10^{-3} \ \text{moles/liter/minute}\) So, the rate of the chemical reaction in moles per liter per minute is \(2.25 \times 10^{-3}\ \text{moles/liter/minute}\).

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction.

When dealing with chemical reactions, it's essential to understand these relationships as they help in predicting how much product will be formed from given amounts of reactants, or vice versa. The core idea is that, due to the conservation of mass, atoms are neither created nor destroyed in a chemical reaction, leading to fixed ratios of reactants and products, described by a balanced chemical equation.

For students, mastering stoichiometry requires a solid grasp of the mole concept and the ability to perform unit conversions effortlessly. The calculation in the exercise we’re discussing here hinges on knowing that stoichiometry can help us transform reaction rates into different time units while preserving the reaction's essential quantitative relationships.

Mole Concept

The mole concept is pivotal in stoichiometry and chemistry at large because it allows chemists to count particles by weighing them. One mole represents Avogadro's number (\(6.022 \times 10^{23}\) particles), and it provides a bridge between the macroscopic amounts of substances we work with in the lab and the microscopic number of atoms or molecules that they contain.

For example, when the exercise mentions a reaction rate of \(2.25 \times 10^{-2}\) moles per liter per second, it's referring to the amount of substance that is reacting every second in terms of moles. By understanding the mole concept, students can better visualize and compute these amounts and their implications for reaction rates.

Unit Conversion

Unit conversion is a fundamental skill in science and everyday life. It allows us to express measurements in different units, which can make calculations more convenient or enable comparisons.

In chemistry, unit conversions often involve the mole concept, as seen in the step-by-step solution of the given exercise. To convert the chemical reaction rate from moles per liter per second to moles per liter per minute, the students were required to recognize that they needed to multiply by the factor of \(60\) since there are \(60\) seconds in a minute. This type of dimensional analysis or unit analysis is a critical tool for ensuring that chemical equations and reaction rate expressions are used accurately in calculations.

Reaction Kinetics

Reaction kinetics is the study of the rates of chemical processes and the factors that affect these rates. Understanding reaction kinetics is essential for controlling how fast reactions occur, which is critical in various applications, such as manufacturing, pharmaceuticals, and environmental processes.

The reaction rate, as provided in the exercise, tells us how quickly the reactants are transformed into products. Knowledge of reaction kinetics also allows scientists to manipulate conditions like temperature, concentration, and catalysts to change these rates. In the context of the given exercise, we see that the rate is measured at a specific temperature (\(322 \text{K}\)), which can be a key factor influencing the speed of the reaction according to the principles of reaction kinetics.