91Ó°ÊÓ

A balanced chemical equation ensures that the number of atoms for each element is equal on both sides of the chemical reaction. This is crucial because it reflects the conservation of mass, meaning matter cannot be created or destroyed. In the reaction to form ammonia, we start with nitrogen gas \( (N_2) \) and hydrogen gas \( (H_2) \), which react to form ammonia \( (NH_3) \). The unbalanced equation initially appears as: \[ N_2(g) + H_2(g) \rightarrow NH_3(g) \] To balance the reaction, adjust the coefficients, which are the numbers before the molecules. The balanced equation becomes: \[ N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \] This indicates that one molecule of nitrogen gas reacts with three molecules of hydrogen gas to produce two molecules of ammonia.

The rate of reaction gives us an idea of how fast or slow a reaction occurs. It is a measure of the change in concentration of reactants or products over time. In chemical kinetics, the rate can often be represented in terms of concentration changes for specific reactants or products in a given period. For ammonia production, the rate of reaction concerning ammonia can be expressed by considering how its concentration changes over time: \[ \text{Rate} = \frac{1}{2} \frac{\Delta [NH_3]}{\Delta t} \] Here, \( \Delta [NH_3] \) represents the change in ammonia concentration, and \( \Delta t \) is the time interval. The factor \( \frac{1}{2} \) arises from the stoichiometry in the balanced equation, indicating that the reaction produces 2 moles of \( NH_3 \) per reaction cycle.

Stoichiometry involves calculating the quantitative relationships between reactants and products in a chemical reaction. It derives directly from the balanced chemical equation. In the context of producing ammonia, the stoichiometry gives us the ratio of hydrogen to ammonia, which is 3:2. This means that for every three moles of hydrogen consumed, two moles of ammonia are produced. Using stoichiometry allows us to relate the rates at which different substances in a reaction are consumed or produced. Knowing the stoichiometric ratios helps calculate other quantities related to the reaction, such as the rates of consumption of other reactants like hydrogen.

Calculating the reaction rate involves determining how fast reactants are converted into products. To find the average rate of reaction for producing ammonia, use the change in concentration divided by the time interval. With the concentration of \( NH_3 \) increasing from 0.257 M to 0.815 M over 15 minutes, the calculation would be: \[ \text{Average rate} = \frac{0.815 - 0.257}{15.0} \] Simplified, this becomes: \[ \text{Average rate} = 0.0372 \text{ M/min} \] Additionally, if we want to determine the rate of hydrogen consumption, use the stoichiometric ratio from the balanced chemical equation. The rate of \( H_2 \) change is: \[ \text{Rate of } \Delta [H_2] = -\frac{3}{2} \times 0.0372 \text{ M/min} \] The negative sign indicates that \( H_2 \) is being consumed: \[ \text{Rate of } \Delta [H_2] = -0.0558 \text{ M/min} \]