Question

For the masses and volumes indicated, calculate the density in grams per cubic centimeter. a. mass \(=4.53 \mathrm{~kg} ;\) volume \(=225 \mathrm{~cm}^{3}\) b. mass \(=26.3 \mathrm{~g} ;\) volume \(=25.0 \mathrm{~mL}\) c. mass \(=1.00\) lb; volume \(=500 . \mathrm{cm}^{3}\) d. mass \(=352 \mathrm{mg} ;\) volume \(=0.271 \mathrm{~cm}^{3}\)

Short answer

The density values for each case are as follows: a) \(Density_a = 20.13 g/cm^3\) b) \(Density_b = 1.052 g/cm^3\) c) \(Density_c = 0.90718 g/cm^3\) d) \(Density_d = 1.29852 g/cm^3\)

Step-by-step solution

Review the Density formula

The formula for density is given as: \[Density = \frac{Mass}{Volume}\] Consistency in units is important. If the units of mass and volume are not consistent, convert them to ensure that mass is in grams (g) and volume is in cubic centimeters (cm^3).

Calculate Density for part a

Given: mass = 4.53 kg, volume = 225 cm^3 First, let's convert the mass from kg to g: \[1 kg = 1000 g\] \[4.53 kg = 4.53 \times 1000 = 4530 g\] Now, use the formula to find the density: \[Density_a = \frac{4530 g}{225 cm^3} = 20.13 g/cm^3\]

Calculate Density for part b

Given: mass = 26.3 g, volume = 25.0 mL First, convert volume from mL to cm^3. Since 1 mL is equal to 1 cm^3: \[25.0 mL = 25.0 cm^3\] Now, use the formula to find the density: \[Density_b = \frac{26.3 g}{25.0 cm^3} = 1.052 g/cm^3\]

Calculate Density for part c

Given: mass = 1.00 lb, volume = 500 cm^3 First, let's convert the mass from lb to g: \[1 lb = 453.592 g\] \[1.00 lb = 1.00 \times 453.592 = 453.592 g\] Now, use the formula to find the density: \[Density_c = \frac{453.592 g}{500 cm^3} = 0.90718 g/cm^3\]

Calculate Density for part d

Given: mass = 352 mg, volume = 0.271 cm^3 First, let's convert the mass from mg to g: \[1 mg = 0.001 g\] \[352 mg = 352 \times 0.001 = 0.352 g\] Now, use the formula to find the density: \[Density_d = \frac{0.352 g}{0.271 cm^3} = 1.29852 g/cm^3\]

Review of Density values for end:

The density values for each case are as follows: a) \(Density_a = 20.13 g/cm^3\) b) \(Density_b = 1.052 g/cm^3\) c) \(Density_c = 0.90718 g/cm^3\) d) \(Density_d = 1.29852 g/cm^3\)

Key concepts

Unit Conversion

Understanding unit conversion is crucial when dealing with measurements in chemistry. Often, you'll need to convert between different units to ensure consistency, particularly in density calculations. Here are some common conversions:

• 1 kilogram (kg) = 1000 grams (g)
• 1 pound (lb) = 453.592 grams (g)
• 1 milliliter (mL) = 1 cubic centimeter (cm³)
• 1 milligram (mg) = 0.001 grams (g)

These conversions help maintain consistency when using the density formula, which often requires mass in grams and volume in cubic centimeters.

Mass and Volume

Mass and volume are foundational concepts in measurement that determine an object's density. Mass refers to the amount of matter in an object, typically measured in grams, kilograms, pounds, or milligrams. Volume measures the space that an object occupies and can be expressed in cubic centimeters or milliliters.
In density calculations, it's crucial to ensure that both mass and volume are in compatible units. This compatibility ensures that the density calculations are accurate and meaningful.
The relationship between mass and volume can also help us understand how different substances compare when considering their density.

Density Formula

The density formula is a simple yet powerful equation used in chemistry to describe how much mass exists in a given volume of a substance. The formula is:\[Density = \frac{Mass}{Volume}\]This formula tells us two main things:

• A substance with a higher mass in a given volume will have a higher density.
• Likewise, if the same amount of mass occupies a larger space, the density will be lower.

By applying the density formula, you can gain insights into the material properties, helping to identify substances or determine quality and consistency.

Measurement in Chemistry

Measurement in chemistry is a key skill and involves precise practices to ensure accuracy and reliability. Measurements must be accurate to obtain valid results, which rely on correctly using units, tools, and understanding conversions.
To ensure the best practices in chemistry measurements, consider:

• Using the right equipment, such as balances for mass and graduated cylinders for volume.
• Understanding and implementing unit conversions when necessary.
• Being attentive to significant figures, especially when handling calculated results from mass and volume data.

All these factors come together to create accurate and dependable measurements, vital for effective density calculation.