Question

In an indoor atmosphere, for \(\mathrm{NO}_{2}\) the value of the first order rate constant has been estimated to be \(1.28 \mathrm{~h}^{-1}\). Calculate its residence time.

Short answer

The residence time for \(\mathrm{NO}_{2}\) is approximately 0.781 hours.

Step-by-step solution

Understanding the Problem

In this exercise, we are given the first-order rate constant for the decay of a compound, nitrogen dioxide (\(\mathrm{NO}_{2}\)). We need to calculate its residence time.

Formula for Residence Time

To calculate the residence time, we need to use the formula for the residence time \( \tau \) which is the inverse of the rate constant \( k \):\[\tau = \frac{1}{k}\]

Substitution

Substitute the given value of the rate constant, \( k = 1.28 \mathrm{~h}^{-1} \), into the formula. We get:\[\tau = \frac{1}{1.28 \mathrm{~h}^{-1}} = 0.78125 \mathrm{~h}\]

Result

The calculated residence time for \(\mathrm{NO}_{2}\) is approximately \(0.781\mathrm{~h}\).

Key concepts

Indoor Air Quality

Indoor air quality is a crucial aspect of environmental chemistry, impacting the well-being and health of individuals who spend a lot of time inside buildings. Poor indoor air quality can be caused by various pollutants such as volatile organic compounds, particulate matter, and gases like nitrogen dioxide (NO₂). Human activities, including cooking and using heating appliances, often contribute to indoor air pollution.
To ensure good indoor air quality:

• Ventilate rooms regularly to reduce pollutant concentration.
• Use air purifiers to filter harmful particles and gases.
• Minimize the use of strong chemical cleaners.
• Keep indoor plants for natural air filtration.

Understanding and maintaining indoor air quality can help reduce health risks such as allergic reactions, respiratory problems, and long-term diseases.

Nitrogen Dioxide

Nitrogen Dioxide, or NO₂, is a significant air pollutant that is particularly concerning in indoor environments. It is a reddish-brown gas with a sharp, biting odor, and can be harmful to both the respiratory system and overall well-being when inhaled over long periods. NO₂ is produced from combustion processes, meaning it is often found in situations where gas appliances are used indoors, such as stoves and heaters.
Potential health effects of Nitrogen Dioxide exposure include:

• Irritation of the eyes, nose, and throat.
• Worsening of existing respiratory diseases like asthma.
• Increased susceptibility to respiratory infections.

Understanding NO₂'s characteristics and sources is essential for managing its presence indoors, especially since it can combine with other chemicals to form dangerous compounds.

First Order Reactions

First order reactions are a type of chemical reaction where the rate of reaction is directly proportional to the concentration of one reactant. This means that when a reaction follows first order kinetics, its rate can be described using a simple equation. For a first order reaction, the rate constant is a value that represents how quickly the reaction proceeds.
The equation that represents a first order reaction is:\[ ext{Rate} = k imes [ ext{A}]\]Where:

• Rate is the rate of the reaction.
• k is the first order rate constant.
• [A] is the concentration of the reactant.

Understanding first order reactions helps in predicting how a pollutant like NO₂ will behave over time in a given environment.

Residence Time

Residence time is an important concept in environmental chemistry, representing the average time a molecule stays in a particular environment before being removed by reaction or dispersion. For first order reactions, residence time is calculated as the inverse of the rate constant, providing insight into how long a pollutant will remain at certain concentrations.
To calculate residence time \( \tau \), the formula is:\[\tau = \frac{1}{k}\]Where:

• \(\tau\) is the residence time in hours (or other time units).
• \(k\) is the rate constant.

In our exercise, the residence time for NO₂, given a rate constant of 1.28 h^-1, is approximately 0.781 hours. This measure helps in planning for ventilation requirements and understanding the potential acute effects of exposure in an indoor environment.