A small airplane takes on 245 L of fuel. If the density of the fuel is \(0.821 \mathrm{~g} / \mathrm{mL},\) what mass of fuel has the airplane taken on? MISSED THIS? Read Section 1.6; Watch KCV 1.6, IWE 1.10

Unit conversion is a fundamental skill in many areas of science and everyday life, enabling us to compare and calculate quantities in different units effectively. In the context of our problem with the airplane's fuel, understanding how to switch from liters to milliliters, and then from grams to kilograms, is crucial. Here's how to make sense of it:
To begin, acknowledge that different units of measurement exist for a reason; they're suited for different scales of values. Liters (L) are typically used for larger volumes, while milliliters (mL) are used for smaller volumes. Knowing that 1 L equals 1000 mL lets us scale up or down between these units effortlessly. Similarly, grams (g) are a smaller unit of mass compared to kilograms (kg). Since 1 kg is the same as 1000 g, this conversion factor lets us express mass in a way that's sometimes easier to interpret, especially for larger quantities like fuel for an airplane.

In our exercise, we're given the volume of fuel in liters, but the density is in grams per milliliter. To work with a consistent set of units, we multiply the volume of the fuel by 1000 to convert liters to milliliters. By doing this, we lay the groundwork for accurate calculation when we apply the mass-volume relationship.

Helpful Tip

Always remember to keep track of your units during conversions. Confusion here can lead to incorrect results. A handy tip is to write down the units at each step of your calculation. This practice helps you to see if units cancel out properly and if your final answer makes sense in the context of the problem.

The mass-volume relationship is at the heart of understanding the properties of substances, especially in chemistry. This concept involves the density of a substance, which tells us how much mass is contained in a given volume. Density is often expressed as grams per milliliter (g/mL) or kilograms per liter (kg/L).

For our airplane's fuel, we're given the density in g/mL, which we can think of as a concentration of mass per unit volume. Mathematically, the density formula is expressed as Density = mass/volume. However, when you're solving for mass, you rearrange the equation to mass = Density x volume. By doing this, you establish a proportional relationship; as the volume of fuel increases or decreases, so does its mass, in direct proportion to its density.

In the exercise, after converting the airplane's fuel volume to the correct units (mL), you can calculate the fuel's mass by multiplying this volume by the fuel's density. The result gives you the mass in grams, pairing the mass and volume units appropriately, thanks to our initial unit conversion.

Importance in Chemistry

This relationship isn't just for fuel calculations; it's fundamental in chemistry for mixing solutions, determining molar masses, and predicting how substances will behave under different conditions. It has broad applications in formulating products, understanding environmental impact, and even cooking.

Chemistry problem-solving is a systematic approach to working through chemical calculations and experiments. The process begins with a clear understanding of the problem, which includes identifying the knowns and unknowns, and the units in which they're expressed. Then you determine the relevant chemical principles – in this case, the mass-volume relationship via density – and choose the appropriate formula to use.

The step-by-step solution we used for the airplane fuel problem is a perfect illustration of problem-solving in action. We started by converting all our measurements to the correct units (liters to milliliters, grams to kilograms). With the units standardized, we then applied the density formula to find the mass of the fuel in grams and eventually converted it to kilograms for a more suitable mass representation for the context.

This logical sequence of steps should be applied to tackle most chemistry problems. By breaking down a complex problem into smaller, manageable parts, we avoid being overwhelmed by the complexity. Detailed note-taking and careful unit tracking are essential, as they prevent common mistakes and ensure that we arrive at the correct solution.

• Understand the problem and its context
• Identify knowns and unknowns
• Standardize units for consistent calculations
• Apply chemical principles and formulas
• Check your work for accuracy and sense

Critical Thinking

Remember, critical thinking is a powerful tool in problem-solving. Question each step, verify your formulas, and consider if the results align with scientific principles and your understanding of the physical world. This thorough approach not only leads to correct answers but also reinforces your grasp of chemistry concepts.