Module #6

Overview of Density, Specific Gravity, Temperature, and Percentage

This set of notes provides an in-depth understanding of important scientific concepts including density, specific gravity, temperature scales, and percentage calculations relevant to chemistry.

Density

Density is a fundamental property defined as the mass of a substance per unit volume, represented mathematically as:Density (D) = Mass (m) / Volume (V)In terms of units, density is often expressed in grams per cubic centimeter (g/cm³) or grams per milliliter (g/mL). Here are the densities of some common substances:

• Ethylene glycol: 1.1 g/cm³

• Water: 1.00 g/cm³

• Ethanol: 0.789 g/cm³

• Copper: 8.94 g/cm³

• Magnesium: 1.738 g/cm³

• Mercury: 13.5 g/cm³

• Gold: 19.3 g/cm³

Calculating Density

Example 1:

To calculate the density of a substance with a mass of 742 grams and a volume of 97.3 cm³, the formula is applied as follows:

• Substitute into the formula: Density = Mass / Volume

• Calculation:

  Density = 742 g / 97.3 cm³ = 7.63 g/mL

Example 2:

If you require 125 grams of a corrosive liquid with a density of 1.32 g/mL, the volume needed can be determined as follows:

• Use the formula: Volume (V) = Mass (m) / Density (d)

• Volume = 125 g / 1.32 g/mL = 94.7 mL

Specific Gravity

Specific gravity is a dimensionless quantity defined as the ratio of the density of a substance to the density of water at 4°C (1.00 g/mL). It can be calculated using:Specific Gravity = Density of Substance / Density of Water

Example 3:

For a 31.10 gram piece of chromium that displaces water from 5.00 mL to 9.32 mL when submerged, the volume of chromium is:Volume of Chromium = 9.32 mL - 5.00 mL = 4.32 mLThe specific gravity is then calculated as: Specific Gravity = Mass of Chromium / Volume of Chromium = 31.10 g / 4.32 mL = 7.20

Temperature Scales

Overview of Temperature

Heat and temperature, while often used interchangeably, are distinct. Temperature is a measure of kinetic energy or thermal energy intensity, while heat is energy transferred between substances.

Common Temperature Scales

The three prevalent temperature scales—Celsius, Fahrenheit, and Kelvin—are based on water's phase transitions:

• Celsius: 0°C (Freezing point), 100°C (Boiling point)

• Fahrenheit: 32°F (Freezing point), 212°F (Boiling point)

• Kelvin: 273 K (Freezing point), 373 K (Boiling point)

Temperature Conversion

From Celsius to Fahrenheit:

The formula to convert Celsius to Fahrenheit is: F = (1.8 * C) + 32

Example 5:

Convert 211°F to Celsius:C = (211 - 32) / 1.8 = 99.4°C

Example 6:

Convert 548 K to Celsius:C = 548 - 273 = 275°C

Heat Transfer and Measurement of Heat

Understanding Heat Transfer

Heat is measured in joules (J) or calories, with 1 calorie equating to approximately 4.184 J.

• Exothermic Process: Releases heat energy.

• Endothermic Process: Absorbs heat energy.

Specific Heat and Heat Capacity

Specific heat is the amount of energy required to raise the temperature of 1 g of a substance by 1°C, while heat capacity relates to a specific quantity (like 1 mol) of a substance.

• Units for specific heat are typically J/g°C and for heat capacity, they are J/°C.

Example 7:

To calculate the heat needed to raise the temperature of 200 g of water from 10.0°C to 55.0°C:Using the equation: q = m * C * ΔT , where ΔT = final temp - initial tempHeat transfer calculation yields q = 200 g * 4.184 J/g°C * (55.0 - 10.0)°C yielding an output in kilojoules.

Synthesis Question

In a practical example, if 1.0 g of seawater contains 4.0 pg of gold, the total gold can be extrapolated from the oceans' total seawater mass to theoretically deduce the height of distributed gold across a given area, incorporating its density for calculations. The analysis provides a glimpse into real-world application of density and mass management in scientific problem-solving.