Problem 138 - General Chemistry

Question

The average flow of the Niagara River is \(3.50 \mathrm{~km}^{3}\) per week. What is this volume in liters?

Step-by-Step Solution

Answer

The volume is 3.50 trillion liters.

Step 1: Convert Cubic Kilometers to Cubic Meters

First, we need to convert the volume from cubic kilometers (kd^3) to cubic meters (mm^3). We know that 1 cubic kilometer is equal to 1 billion cubic meters (= 10^9 m^3). Therefore, the average flow in cubic meters is calculated by \(3.50 \, \text{km}^3 \times 10^9 = 3.50 \times 10^9 \, \text{m}^3\).

Step 2: Convert Cubic Meters to Liters

Since 1 cubic meter is equal to 1,000 liters, we can convert the volume from cubic meters to liters by multiplying by 1,000. Thus, the average flow in liters is \(3.50 \times 10^9 \, \text{m}^3 \times 1,000 = 3.50 \times 10^{12}\) liters.

Key Concepts

Understanding Conversion: Cubic Kilometers to Cubic Meters

Volume conversion is an essential concept in many scientific fields, including physics and chemistry. One common conversion is from cubic kilometers (km³) to cubic meters (m³). Imagine a large container the size of a kilometer cube. To convert volumes at such a scale, it's helpful to remember that 1 km³ is equal to 1 billion m³. This is because:

• 1 kilometer equals 1,000 meters.
• So, \(1 ext{ km}^3 = (1,000 ext{ m})^3 = 1,000^3 ext{ m}^3 = 1,000,000,000 ext{ m}^3\).

By understanding this, you can easily convert any volume from cubic kilometers to cubic meters simply by multiplying by 10⁹. For example, if the average volume of water flowing in the Niagara River is 3.50 km³ per week, the equivalent in cubic meters would be:\(3.50 ext{ km}^3 imes 10^9 = 3.50 imes 10^9 ext{ m}^3\).This step forms the foundation for many subsequent conversions, like moving from m³ to liters.

From Cubic Meters to Liters: A Simple Step

Converting cubic meters (m³) to liters is a straightforward process. This conversion is frequently used in science, especially chemistry, where liters are a common unit of volume. The key fact to remember is that:

• 1 cubic meter is equal to 1,000 liters.

This means that when you have a volume in cubic meters, you simply multiply by 1,000 to convert to liters. For our example with the Niagara River's flow:\(3.50 imes 10^9 ext{ m}^3 imes 1,000 = 3.50 imes 10^{12} ext{ liters}\).Making quick work of such conversions helps streamline calculations, allowing you to work effectively with different units in scientific equations and real-world applications.

Unit Conversion in Chemistry

Unit conversion is fundamental in chemistry, as it allows scientists to communicate measurements consistently and accurately. Chemistry often involves measuring and converting volumes, which is why understanding the conversions between cubic kilometers, cubic meters, and liters is crucial. When measuring large volumes, such as in industrial processes or natural phenomena, starting with cubic kilometers or cubic meters is common.

• Cubic kilometers are usually reserved for very large-scale measurements, like oceans or rivers.
• Cubic meters offer a middle ground for things like tanks or larger lab experiments.
• Liters are used for manageable quantities, like those often found in experimental procedures.

Knowing how to switch between these units lets chemists precisely manipulate their data, ensuring results remain reliable and comparable. This skill is also invaluable for converting other units of measurement, from mass to concentration, often encountered in daily chemical calculations.