91Ó°ÊÓ

Stoichiometry is a fundamental concept in chemistry, focusing on the quantitative relationships between reactants and products in a chemical reaction. It allows us to determine how much of each substance is needed or produced. The given reaction: \[ \text{HOCH}_{2} \text{CH}_{2} \text{OH} + 2 \text{HNO}_{2} \rightarrow \text{NO}_{2}-\text{CH}_{2} \text{CH}_{2} \text{NO}_{2} + 2 \text{H}_{2} \text{O} \] shows that:

• 2 moles of \(\text{HNO}_{2}\) react with 1 mole of \(\text{HOCH}_{2}\text{CH}_{2}\text{OH}\).
• 1 mole of \(\text{NO}_{2}-\text{CH}_{2}\text{CH}_{2}\text{NO}_{2}\) and 2 moles of \(\text{H}_{2}\text{O}\) are produced.

Understanding stoichiometry is crucial because it allows us to calculate how much of each substance disappears or appears during the reaction. Through stoichiometry, we find the exact proportions in which chemicals react and form products.

The rate of reaction is a measure of how quickly reactants are turned into products over time. In this scenario, the rate of reaction for \(\text{HNO}_{2}\) is given as \(-0.045\) mol/s, indicating it's consumed at this rate. This rate is an essential descriptor of the chemical kinetics involved in the reaction. The rate of reaction helps:

• Determine how quickly a reactant is used up or a product is formed.
• Understand the behavior of the reaction over time.

Moreover, the rate at which a reaction occurs depends on several factors like concentration, temperature, and catalysts. These aspects affect the speed at which molecules collide and react. Thus, having the rate of reaction helps in optimizing conditions for desired reaction speeds.

The disappearance rate in a chemical reaction refers to the speed at which a reactant is consumed. For the given exercise, the rate of disappearance of \(\text{HNO}_{2}\) is \(-0.045\) mol/s. This negative sign indicates a reduction in the concentration of this reactant over time.The disappearance rate also applies to other reactants in proportion to their stoichiometric relationship. For \(\text{HOCH}_{2}\text{CH}_{2}\text{OH}\), with its one-to-two molar ratio with \(\text{HNO}_{2}\), the rate is calculated by: \[ \text{Rate of disappearance of } \text{HOCH}_{2}\text{CH}_{2}\text{OH} = -\frac{1}{2} \times (-0.045) = 0.0225 \text{ mol/s} \] Understanding disappearance rates aids in gauging how fast reactants diminish, impacting how long a reaction might last or how it needs to be adjusted for efficiency.

Appearance rate refers to the rate at which a product is formed in a chemical reaction. In this exercise, we can calculate the appearance rates for \(\text{NO}_{2}-\text{CH}_{2}\text{CH}_{2}\text{NO}_{2}\) and \(\text{H}_{2}\text{O}\) based on stoichiometry relative to the disappearance of \(\text{HNO}_{2}\).

• For \(\text{NO}_{2}-\text{CH}_{2}\text{CH}_{2}\text{NO}_{2}\), each mole corresponds to 2 moles of \(\text{HNO}_{2}\) consumed, giving us: \\[ \text{Rate of appearance of } \text{NO}_{2}-\text{CH}_{2}\text{CH}_{2}\text{NO}_{2} = \frac{1}{2} \times 0.045 = 0.0225 \text{ mol/s} \]
• For \(\text{H}_{2}\text{O}\), since 2 moles are formed for each 2 moles of \(\text{HNO}_{2}\), the rate is the same as \(\text{HNO}_{2}\): \\[ \text{Rate of appearance of } \text{H}_{2}\text{O} = 0.045 \text{ mol/s} \]

Appearance rates are vital for understanding how quickly products form, important in industrial applications where product yield and time are critical factors.