Question

Average ozone concentrations in jakarta, Indonesia have been reported to be \(0.015 \mathrm{mg} \mathrm{m}^{-3}\) and those in Tokyo, lapan are \(20 \mathrm{ppbv}\). What is the approximate ratio of these two values, when expressed in the same units?

Short answer

The ratio is approximately 0.383, meaning Tokyo's ozone concentration is higher than Jakarta's.

Step-by-step solution

Understand Units

First, we need to understand the units given. Jakarta's concentration is given in \(\text{mg}\, \text{m}^{-3}\) which is a mass per volume unit, while Tokyo's concentration is given in \(\text{ppbv}\), which stands for parts per billion by volume, commonly used in atmospheric science to represent gas concentrations.

Convert ppbv to mg/m³

To convert \(\text{ppbv}\) to \(\text{mg}\, \text{m}^{-3}\), we use the relationship that 1 \(\text{ppbv}\) is approximately \(1.96 \times 10^{-3}\, \text{mg/m}^3\) at standard conditions for air (assuming ideal gas behavior). Therefore, we calculate the conversion for Tokyo's concentration: \(20 \times 1.96 \times 10^{-3} = 0.0392 \text{mg/m}^3\).

Calculate the Ratio

Now that both values are in the same unit, \(\text{mg/m}^3\), we can find the ratio between them. Jakarta's concentration is \(0.015 \text{mg/m}^3\) and Tokyo's converted concentration is \(0.0392 \text{mg/m}^3\). Thus the ratio of Jakarta to Tokyo is: \( \frac{0.015}{0.0392} \approx 0.383\).

Interpret the Ratio

The approximate ratio of the ozone concentration in Jakarta compared to Tokyo, when both are expressed in \(\text{mg/m}^3\), is \(0.383\). This means Tokyo's ozone concentration is higher than Jakarta's when compared in the same unit.

Key concepts

Ozone Concentration

Ozone concentration is a measure of how much ozone (O\(_3\)) is present in the air. Ozone is a gas that occurs both at the ground level and in the Earth's upper atmosphere. Depending on its location, ozone can be good or bad for you and the environment.
Ground-level ozone, also called tropospheric ozone, is a key component of smog. In contrast, the ozone layer in the stratosphere protects us from the sun's harmful ultraviolet rays.
Ozone concentration is typically measured in terms of mass per volume or volume per volume. Common units include

• milligrams per cubic meter (mg/m\(^3\)), a mass per volume unit
• parts per billion by volume (ppbv), a volume-based measure

Understanding these units is essential for comparing ozone levels across different reports or regions.

Unit Conversion

Unit conversion is the process of converting a measurement from one unit to another. It is an essential skill in environmental chemistry, allowing scientists to compare and analyze data accurately.
When dealing with ozone measurements, it's crucial to know how to convert between units like mg/m\(^3\) and ppbv, which represent different aspects of concentration.
This conversion often involves understanding the conditions under which measurements are taken, such as temperature and pressure. For ozone and other gases, conversions are based on standard conditions (25°C and 1 atm). One common conversion factor used is that 1 ppbv is approximately 1.96 x 10\(^{-3}\) mg/m\(^3\) at standard conditions.

Atmospheric Science

Atmospheric science encompasses the study of the Earth's atmosphere and its various components, including gases like ozone. This field examines the dynamics of weather and climate, as well as air quality issues.
Understanding atmospheric processes is critical for interpreting ozone levels, as these levels are influenced by factors such as

• solar radiation
• emissions from vehicles and industry
• natural phenomena like wildfires and volcanic activity

Researchers in atmospheric science work to understand how these factors interact to affect weather patterns and climate, and what implications these interactions have for air quality and human health.

Gas Concentrations

Gas concentrations tell us how much of a particular gas is present in a given volume of air. Atmospheric gases like ozone are typically measured in small concentrations, necessitating units like

• ppbv (parts per billion by volume), which indicate the number of molecules of a gas per billion molecules of the air
• mg/m\(^3\) (milligrams per cubic meter), which describe the mass of the gas in a cubic meter of air

Such measurements help assess environmental conditions and pollutants' impacts on health and climate. Accurately measuring and reporting these concentrations is key to informed environmental management and policy-making.

Ideal Gas Behavior

Ideal gas behavior refers to the way gases theoretically behave under certain conditions of temperature and pressure, following the ideal gas law: \[ PV = nRT \]
where

• \(P\) is pressure
• \(V\) is volume
• \(n\) is the number of moles of gas
• \(R\) is the universal gas constant
• \(T\) is temperature in Kelvin

In reality, gases don't always behave ideally, especially under high pressure or low temperature. However, the ideal gas law provides a good approximation for understanding and converting gas concentrations, especially for conditions near standard temperature and pressure (0°C and 1 atm).
This concept is particularly useful for converting units like ppbv to mg/m\(^3\), as it helps account for the changes in gas volume with temperature and pressure shifts.