Problem 8 - Chemistry: Principles and Reactions

Question

Ammonia is produced by the reaction between nitrogen and hydro- gen gases. (a) Write a balanced equation using smallest whole-number coefficients for the reaction. (b) Write an expression for the rate of reaction in terms of \(\Delta\left[\mathrm{NH}_{3}\right]\). (c) The concentration of ammonia increases from \(0.257 \mathrm{M}\) to \(0.815 \mathrm{M}\) in \(15.0 \mathrm{~min} .\) Calculate the average rate of reaction over this time interval.

Step-by-Step Solution

Answer

Answer: The average rate of reaction is \(6.2 \times 10^{-4} \frac{\mathrm{M}}{\mathrm{s}}\).

Step 1: Write the balanced equation for the reaction

To produce ammonia (NH3), nitrogen (N2) reacts with hydrogen (H2) in the given proportion: N2 + 3H2 -> 2NH3

Step 2: Write an expression for the rate of reaction

The rate of reaction is the change in the concentration of ammonia over the change in time. We can represent the rate of reaction (r) as follows: \[r = \frac{\Delta\left[\mathrm{NH}_{3}\right]}{\Delta t}\]

Step 3: Calculate the initial and final concentrations of ammonia

The initial concentration of ammonia is 0.257 M and the final concentration is 0.815 M.

Step 4: Calculate the change in concentration of ammonia

We need to find the difference between the initial and final concentrations: \[\Delta\left[\mathrm{NH}_{3}\right] = \text{Final concentration} - \text{Initial concentration}\] \[\Delta\left[\mathrm{NH}_{3}\right] = 0.815\mathrm{M} - 0.257\mathrm{M}\] \[\Delta\left[\mathrm{NH}_{3}\right] = 0.558\mathrm{M}\]

Step 5: Convert the time interval to seconds

The time interval given is 15.0 minutes. Converting it to seconds: \[15.0\text{ minutes} \times \frac{60\text{ seconds}}{1\text{ minute}} = 900\text{ seconds}\]

Step 6: Calculate the average rate of reaction

Now we can plug the change in concentration of ammonia and the time interval into the rate of reaction formula: \[r = \frac{0.558\mathrm{M}}{900\mathrm{s}}\] \[r = 6.2 \times 10^{-4} \frac{\mathrm{M}}{\mathrm{s}}\] The average rate of reaction over this time interval is \(6.2 \times 10^{-4} \frac{\mathrm{M}}{\mathrm{s}}\).

Key Concepts

Balanced Chemical Equation

In chemical reactions, a balanced chemical equation is crucial. It represents the conservation of mass, which tells us that atoms are neither created nor destroyed in a chemical reaction, only rearranged. For the production of ammonia, the reaction involves nitrogen (\(\text{N}_2\)) and hydrogen (\(\text{H}_2\)) combining to form ammonia (\(\text{NH}_3\)). The balanced equation is:\[\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3\]This equation shows that one molecule of nitrogen reacts with three molecules of hydrogen to produce two molecules of ammonia.

• The coefficients (numbers before the molecules) are the smallest whole numbers that balance the atoms on both sides of the equation.
• Balancing ensures that the number of atoms for each element is equal on both the reactant and product sides.

The balanced equation is foundational as it helps chemists understand the proportions of reactants needed and the products formed.

Rate of Reaction

The rate of reaction is a measure of how quickly a chemical reaction occurs. It can be defined as the change in concentration of a reactant or product per unit time. In the case of ammonia production, we express the rate in terms of ammonia's concentration change:\[r = \frac{\Delta\left[\text{NH}_3\right]}{\Delta t}\]

• \(\Delta\left[\text{NH}_3\right]\) denotes the change in concentration of ammonia.
• \(\Delta t\) represents the change in time.

Understanding the rate of reaction helps scientists predict how long a reaction will take under given conditions. It also provides insights into the reaction's mechanism and the effect of changing conditions such as temperature or concentration.

Reaction Rate Calculation

Calculating the reaction rate involves determining how much a product's concentration changes over a specified period of time. For ammonia production, the concentration change and time interval are crucial.Given that the concentration of ammonia increases from 0.257 M to 0.815 M over 15.0 minutes, we find:- **Change in concentration (\(\Delta\left[\text{NH}_3\right]\))**: \[ \Delta\left[\text{NH}_3\right] = 0.815 \,\text{M} - 0.257 \,\text{M} = 0.558 \,\text{M} \]- **Time in seconds**: \[15.0 \,\text{minutes} \times \frac{60 \,\text{seconds}}{1 \,\text{minute}} = 900 \,\text{seconds} \]With these, the average reaction rate is:\[ r = \frac{0.558 \,\text{M}}{900 \,\text{s}} = 6.2 \times 10^{-4} \,\frac{\text{M}}{\text{s}} \]This value signifies the rate at which the concentration of ammonia changes over the given time interval, providing a clear picture of the reaction's dynamics.