Problem 82 - General Chemistry: Principles and Modern Applications

Question

A Boeing 767 due to fly from Montreal to Edmonton required refueling. Because the fuel gauge on the aircraft was not working, a mechanic used a dipstick to determine that 7682 L of fuel were left on the plane. The plane required \(22,300 \mathrm{kg}\) of fuel to make the trip. In order to determine the volume of fuel required, the pilot asked for the conversion factor needed to convert a volume of fuel to a mass of fuel. The mechanic gave the factor as \(1.77 .\) Assuming that this factor was in metric units (kg/L), the pilot calculated the volume to be added as 4916 L. This volume of fuel was added and the 767 subsequently ran out the fuel, but landed safely by gliding into Gimli Airport near Winnipeg. The error arose because the factor 1.77 was in units of pounds per liter. What volume of fuel should have been added?

Step-by-Step Solution

Answer

The plane should have been loaded with an additional fuel volume of approximately 20,100 liters.

Step 1: Calculation of Fuel Volume in Proper Units

The first step is to convert the weight of the required fuel from kilograms to pounds, since the provided conversion factor is in pounds per liter. Here's how this can be done:We know that 1 kg is approximately 2.20462 pounds. So we multiply 22,300 kg, the total weight required for the trip, by this factor to convert it to pounds.\[22,300 \mathrm{kg} \times 2.20462 \mathrm{lb/kg} = 49,172.966 \mathrm{lb}\]

Step 2: Calculation of Required Fuel Volume

Now that we have the weight in pounds, we can divide it by the correct conversion factor (1.77 lb/L) to find the required fuel volume:\[49,172.966 \mathrm{lb} \div 1.77 \mathrm{lb/L} = 27,781.87 \mathrm{L}\]

Step 3: Calculation of Additional Required Fuel After Considering Initial Fuel Volume

The calculation above gives us the total volume of the fuel required for the trip. However, we must subtract from this the volume of the fuel that was already in the plane (7682 L) to find out how much extra fuel was needed:\[27,781.87 \mathrm{L} - 7682 \mathrm{L} = 20,099.87 \mathrm{L}\]

Key Concepts

Metric Conversion Errors

Metric conversion errors can have significant consequences, especially in industries such as aviation where precision is crucial. When dealing with fuel, which is essential for aircraft operation, a miscalculation can lead to situations like running out of fuel mid-flight.

Metric conversions often involve changing a measurement from one unit to another. This seems straightforward but can become complex when dealing with different systems, like converting between kilograms and pounds or liters and gallons. In the original exercise, the confusion arose because the conversion factor provided by the mechanic was in pounds per liter, while the pilot assumed it was in kilograms per liter.

• Always confirm the units involved in a conversion factor.
• Utilize conversion factors accurately, taking care to convert all necessary measurements to the correct unit system.
• Whenever possible, double-check with another source or a backup system to ensure no conversion errors occur.

By paying attention to these details and verifying conversion details, errors can be reduced, ensuring both efficiency and safety.

Fuel Volume Calculation

Calculating the accurate volume of fuel needed for a flight involves a few steps. First, knowing the weight of fuel required in the correct unit is essential. In this situation, the Boeing 767 required 22,300 kg of fuel, but the conversion factor needed was in pounds per liter. This required converting kilograms to pounds.

Once the weight is determined, the next step is to use the conversion factor correctly to calculate the volume. The exercise demonstrated this process by using the conversion factor of 1.77 (pounds per liter):

• Convert 22,300 kg to pounds, using 1 kg = 2.20462 lbs.
• Calculating the volume: Divide the total required pounds by the conversion factor to find the volume of fuel needed in liters.

Accurate calculations directly impact flight safety and efficiency, and following proper conversion steps ensures that the aircraft has the appropriate fuel volume for its journey.

Aviation Fuel Requirements

Fuel requirements for a flight aren't just about filling the tank. They involve detailed planning and precise calculations to achieve optimal balance and safety. Aviation fuel calculations consider the distance, weight of the aircraft, and current fuel volume.

In the given situation, the aircraft needed additional fuel to meet its target weight requirement after evaluating the existing amount. Initially, it had 7,682 liters, and after determining the total needed was roughly 27,781.87 liters based on conversion calculations, the extra fuel amount needed was significant.

• Always know the starting fuel volume before calculating additional needs.
• Include extra fuel for safety—usually calculated as a reserve in case of unforeseen circumstances like diverting to another airport.
• Maintain communication between ground crew and flight crew to ensure all calculations align.

Understanding aviation fuel requirements means accounting for everything from the weight of the aircraft to the final destination to ensure a safe and efficient trip.