Textbook Question
Two spheres of equal volume are placed on the scales as shown. a. Which one is more dense?
Ch.1 - Introduction: Matter, Energy, and Measurement
Chapter 1, Problem 87
The mass of an empty oil drum is listed as 2.0×104 g. After a quantity of biodiesel fuel is added to the drum, the total mass is 7.05×105 g.
a. To how many significant figures should the mass of the biodiesel in the drum be reported?
b. The density of the biodiesel fuel is 0.875 g/cm3. What is the volume of biodiesel that has been added to the drum, in L?
Verified step by step guidance1
Step 1: Calculate the mass of the biodiesel by subtracting the mass of the empty drum from the total mass. Use the formula: \( \text{Mass of biodiesel} = \text{Total mass} - \text{Mass of empty drum} \).
Step 2: Determine the number of significant figures for the mass of the biodiesel. The mass of the empty drum is given as 2.0×104 g (2 significant figures) and the total mass is 7.05×105 g (3 significant figures). The result should be reported with the least number of significant figures from the given values.
Step 3: Use the density formula to find the volume of the biodiesel. The formula is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Rearrange it to solve for volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
Step 4: Substitute the mass of the biodiesel and the density (0.875 g/cm3) into the volume formula to calculate the volume in cm3.
Step 5: Convert the volume from cm3 to liters. Remember that 1 L = 1000 cm3.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Significant Figures
Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When performing calculations, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures to ensure accuracy.
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Significant Figures Example
Density
Density is defined as mass per unit volume and is typically expressed in units such as grams per cubic centimeter (g/cm³) or kilograms per liter (kg/L). It is a crucial property that helps in converting between mass and volume. In this context, knowing the density of biodiesel allows us to calculate the volume of the fuel added to the drum based on its mass.
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Volume Calculation
Volume can be calculated using the formula: Volume = Mass / Density. This relationship allows us to determine how much space a substance occupies based on its mass and density. In the case of the biodiesel, once the mass is determined, applying this formula will yield the volume in liters, which is essential for understanding how much fuel has been added to the drum.
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Related Practice
Textbook Question
Water has a density of 0.997 g/cm3 at 25 °C; ice has a density of 0.917 g/cm3 at -10 °C. (a) If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 °C, what volume does the ice occupy? (b) Can the ice be contained within the bottle?
Textbook Question
A 32.65-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 mL. The solid and toluene together weigh 58.58 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?
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Textbook Question
Automobile batteries contain sulfuric acid, which is commonly referred to as “battery acid.” Calculate the number of grams of sulfuric acid in 1.00 gal of battery acid if the solution has a density of 1.28 g/mL and is 38.1% sulfuric acid by mass.