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Heat Equation and Significant Figures

• Always list what you know and what you don't know for problems.
• Use proper notation for clarity, preferably scientific notation for large/small numbers.
• Key Concepts in Significant Figures:
  • Operations:
  • For addition and subtraction, the result should have the same number of decimal places as the term with the least decimal places.
  • For multiplication and division, the result should have the same number of significant figures as the term with the least significant figures.

Given Problem Example:

• A beaker contains 250.0 grams of water:
• Added Heat (Q): 1,500.0 Joules
• Initial Temp (Tᵢ): 22.0 °C
• Final Temp (Tₓ): 23.44 °C

Task: Find the specific heat capacity (C)

1. Relevant Formula: Q = mC(Tf - Ti)
   • Rearrange to find:
     C = \frac{Q}{m \cdot (Tf - Ti)}

Calculation Steps:

• Compute temperature change:
  • \Delta T = Tf - Ti = 23.44 °C - 22.0 °C = 1.44 °C
• Substitute into the formula:
  • C = \frac{1500.0 \text{ J}}{250.0 ext{ g} \cdot 1.44 °C}
  • Cancel units to get C in J/g°C.

Significant Figures Analysis:

• Q = 1500.0 ext{ J} has 5 sig figs.
• m = 250.0 ext{ g} also has 4 sig figs.
• \Delta T = 1.44 °C has 3 sig figs.
• Final result should consider the least significant figure = 3 sig figs.

Energy Values and Nutrition - Section 3.5

• Learning Objectives: Calculate energy values for food molecules (carbohydrates, fats, proteins) using a conversion table which can be found on a periodic table in the exam.
• Nutritional calories (Dietary calories) represent energy from food. Conversion between food calories and scientific calories:
  • 1 ext{ kcal} = 1000 ext{ calories}

Example Problem:

• A food label states:
  • Fat Energy Content: 9 food calories/gram
  • Convert 3.45 grams of fat to Joules.
  1. Set up conversion:
  2. 3.45 ext{ g fat} \times \frac{9 ext{ kcal}}{1 ext{ g fat}} \times \frac{1000 ext{ calories}}{1 ext{ kcal}} \times \frac{4.184 ext{ J}}{1 ext{ calorie}}
  3. Result in Joules: Use significant figures appropriately to convert.

Kilocalories for Food Analysis

• Common macronutrient conversion:
  • Carbohydrates: 4 kcal/g
  • Fats: 9 kcal/g
  • Proteins: 4 kcal/g

Example with Cheeseburger:

• Contains:
  • 22 g Carbohydrates, 15 g Fat, 10 g Protein.
• Calculate total kcal:
  1. Carbs: 22 g \times 4 ext{ kcal/g} = 88 ext{ kcal}
  2. Fat: 15 g \times 9 ext{ kcal/g} = 135 ext{ kcal}
  3. Protein: 10 g \times 4 ext{ kcal/g} = 40 ext{ kcal}
  4. Total: 88 + 135 + 40 = 263 ext{ kcal}
• When adding, allow for the least number of decimal places (1).

Periodic Table and Atomic Structure

• Sections: Elements and symbols (4.1), Periodic table (4.2)
• Periodic Table Arrangement:
  • Elements arranged by increasing atomic number (number of protons).
  • Predicted existence of subsequent elements based on previous properties.

Key Components of Periodic Table:

• Atomic Number: Number of protons, always an integer;
• Element Symbology:
  • Consists of 1 or 2 letters (first letter always capitalized, second lower case).
• Atomic Mass: Average mass of isotopes, usually a decimal.
• Recognize isotopes: atoms of an element with different masses but the same chemical properties.

Final Considerations for Exam Preparation

• Review significant figures in all calculations.
• Understand the conversion factors between Joules, calories, and kilocalories.
• Utilize the chemical symbol chart and periodic table.
• Those topics covered in PowerPoint 1 and 2 will be on Exam 1 due on April 22, while PowerPoint 3 will not be on Exam 1.