Problem 90 - General Chemistry

Question

The estimated amount of recoverable oil from the field at Prudhoe Bay in Alaska is \(1.3 \times 10^{10}\) barrels. What is this amount of oil in cubic meters? One barrel \(=42 \mathrm{gal}\) \((\) exact \(), 1 \mathrm{gal}=4\) qt (exact), and \(1 \mathrm{qt}=9.46 \times 10^{-4} \mathrm{~m}^{3}\).

Step-by-Step Solution

Answer

The amount of oil in cubic meters is approximately \(2.07 \times 10^9\) m³.

Step 1: Convert Barrels to Gallons

To convert the estimated amount of oil from barrels to gallons, use the conversion factor that 1 barrel equals 42 gallons. Thus,\[\text{Total gallons} = 1.3 \times 10^{10} \text{ barrels} \times 42 \text{ gallons/barrel} = 5.46 \times 10^{11} \text{ gallons} \]

Step 2: Convert Gallons to Quarts

Next, convert the total gallons obtained in Step 1 to quarts using the conversion factor of 1 gallon equals 4 quarts. Thus,\[\text{Total quarts} = 5.46 \times 10^{11} \text{ gallons} \times 4 \text{ quarts/gallon} = 2.184 \times 10^{12} \text{ quarts} \]

Step 3: Convert Quarts to Cubic Meters

Finally, convert the total quarts to cubic meters using the given conversion factor, where 1 quart equals \(9.46 \times 10^{-4} \text{ m}^3\). So,\[\text{Total cubic meters} = 2.184 \times 10^{12} \text{ quarts} \times 9.46 \times 10^{-4} \text{ m}^3/ ext{quart} = 2.065584 \times 10^9 \text{ m}^3\]

Key Concepts

Understanding Cubic Meters

Cubic meters, often denoted as \( ext{m}^3 \), are a standard unit of volume in the metric system. They are used extensively across various fields such as construction, shipping, and chemistry. A cubic meter is a cube whose surface is one meter long in each dimension. This means it is a great way to measure large volumes of materials, such as oil, water, or gas.

In everyday life, cubic meters can seem quite large because they often represent industrial quantities or scientific measurements. For example, an average bathtub holds approximately 0.15 cubic meters of water when full. Understanding the scale of a cubic meter helps visualize and compare it to smaller units like liters or milliliters, where 1 cubic meter equals 1,000 liters or 1,000,000 milliliters.

This unit is particularly handy in scientific contexts like chemistry, where thorough and precise volume measurements are crucial. Whether working with gases, liquids, or solids, knowing the volume in cubic meters allows for accurate chemical calculations.

The Process of Volume Conversion

Volume conversion is a process of changing the measurement of volume from one unit to another. In real-world applications, multiple conversion steps may be necessary, much as in the original exercise.

Let's break it down into simple steps:

• Identifying the Conversion Path: Determine which units you begin with and what units you need as your final measurement.
• Utilizing Conversion Factors: Make sure you know the correct conversion factors, such as 1 barrel = 42 gallons, and 1 quart = \(9.46 \times 10^{-4} \text{ m}^3\). These factors act as a bridge from one unit to another.
• Performing Multiplicative Calculations: Use multiplication to convert your original unit step-by-step to reach the desired unit. A consistent approach helps prevent errors during the process.

Each step is necessary to transition smoothly between units, ensuring that the converted volume remains accurate. This is significant in fields like chemistry, where precision is key.

The Importance of Measurement in Chemistry

In chemistry, measurement is everything. Accurate measurements of substances allow chemists to perform calculations, predict reactions, and understand material properties. Volume measurements are a core aspect due to their relevance in reactions involving liquids and gases.

Here are some reasons why accurate measurement is crucial:

• Reaction Stoichiometry: Knowing the exact volume of reactants helps predict the quantities of products formed in a chemical reaction.
• Concentration Calculations: Volume measurements are essential for calculating the concentration of solutions, which are often in units like mol/L.
• Safe Handling of Chemicals: Knowledge of volume helps ensure safe handling and storage of chemicals, preventing spills and accidents.

Understanding the importance of precise volume measurement helps not just in lab scenarios but also in industrial applications, ensuring safety, efficiency, and accuracy in chemical processes.