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CHE 141 Chapter E EoC problems Part 1

David Magers・32 minutes read

The text provides various temperature and measurement conversions, including converting Fahrenheit to Celsius and Kelvin, and metric conversions between units like liters to milliliters and grams to gigagrams. Additionally, it discusses significant digits in calculations and gives examples of density calculations for materials like pennies and glycerol.

Insights

  • Converting temperatures and measurements involves straightforward formulas and methods that can yield significant insights, such as how 32°F is the freezing point of water at 0°C, illustrating the importance of understanding temperature conversions in everyday contexts. Additionally, the text emphasizes the concept of significant digits in calculations, highlighting that precision matters; for instance, when multiplying 27.5 by 1.82, the result must be rounded to reflect the least number of significant digits in the original numbers, which is crucial for accurate scientific communication and data representation.

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Recent questions

  • What is the freezing point of water?

    The freezing point of water is 0°C, which is equivalent to 32°F. This temperature is significant as it marks the transition from liquid to solid for water, a fundamental property that is crucial in various scientific and everyday contexts. Understanding this point is essential for activities such as cooking, weather forecasting, and studying climate patterns. The freezing point can also be influenced by factors such as pressure, but under standard atmospheric conditions, it remains a constant reference point in temperature scales.

  • How do you convert Fahrenheit to Celsius?

    To convert Fahrenheit to Celsius, you can use the formula: (Fahrenheit temperature - 32) / 1.8. This formula allows you to accurately translate temperatures from the Fahrenheit scale, commonly used in the United States, to the Celsius scale, which is used in most other countries. For example, if you have a temperature of 68°F, you would subtract 32 to get 36, and then divide by 1.8, resulting in approximately 20°C. This conversion is particularly useful in scientific contexts, cooking, and when traveling to countries that use the Celsius system.

  • What is the formula for converting Kelvin to Celsius?

    The formula for converting Kelvin to Celsius is straightforward: subtract 273 from the Kelvin temperature. For instance, if you have a temperature of 300 K, you would calculate 300 - 273, resulting in 27°C. This conversion is essential in scientific fields, particularly in thermodynamics and physical chemistry, where temperature measurements are often taken in Kelvin. Understanding this conversion helps in interpreting data and conducting experiments that require precise temperature readings.

  • How do you convert liters to milliliters?

    To convert liters to milliliters, you simply multiply the number of liters by 1,000. For example, if you have 2 liters of a liquid, you would calculate 2 × 1,000, resulting in 2,000 milliliters. This conversion is commonly used in cooking, chemistry, and various industries where precise liquid measurements are necessary. Knowing how to convert between these two units is crucial for accurate dosing, mixing solutions, and understanding product volumes in recipes or scientific experiments.

  • What is the significance of significant digits?

    Significant digits, or significant figures, are important in scientific measurements as they convey the precision of a number. They include all the non-zero digits, any zeros between them, and any trailing zeros in a decimal number. For example, in the number 0.00456, there are three significant digits (4, 5, and 6). Understanding significant digits is crucial for reporting measurements accurately, as it helps to communicate the reliability of the data. In calculations, the result should be reported with the same number of significant digits as the least precise measurement used in the calculation, ensuring that the precision of the data is maintained.

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Summary

00:00

Temperature and Measurement Conversion Guide

  • Convert 32°F to Celsius: 32°F equals 0°C, the freezing point of water, requiring no formula for conversion.
  • Convert 77 K to Celsius: 77 K minus 273 equals -196°C; then convert to Fahrenheit using the formula: -196°C × 1.8 + 32 equals -321°F.
  • Convert 109°F to Celsius: Use the formula (109°F - 32) / 1.8, resulting in 78.3°C.
  • Convert 98.6°F (body temperature) to Celsius: (98.6°F - 32) / 1.8 equals 37.0°C; then add 273.15 to get 310.15 K, rounded to 310.2 K.
  • Convert 80°F (coldest US temperature) to Celsius: (80°F - 32) / 1.8 equals -62°C; add 273 to get 211 K, rounded to 21 K.
  • Use prefix multipliers for problem 23: 3.4 × 10^-6 m equals 3.4 micrometers; 11 × 10^-12 s equals 11 picoseconds; 7.4 × 10^3 g equals 7.4 kilograms.
  • Convert 12.1 × 10^8 g to gigagrams: Rewrite as 1.21 × 10^9 g, which equals 1.21 gigagrams.
  • Convert 4.5 ns to seconds: 4.5 ns equals 4.5 × 10^-9 s; 18 ftos equals 18 × 10^-15 s, or 1.8 × 10^-14 s in scientific notation.
  • Convert 515 km to decimeters: 515 km equals 5.15 × 10^6 dm; convert 122.355 s to milliseconds: 122.355 s equals 1.22355 × 10^5 ms.
  • Convert 10,245.5 m to kilometers: 10,245.5 m equals 10.2455 km; convert to megameters: 10,245.5 m equals 0.0102455 Mm.

22:11

Measurement Conversions and Significant Digits Explained

  • To convert 12,455 meters to millimeters, multiply by 1,000, resulting in 12,455,000 mm or 1.2455 x 10^7 mm in scientific notation.
  • Converting 12,455 meters to centimeters involves multiplying by 100, yielding 1,245,500 cm or 1.2455 x 10^6 cm in scientific notation.
  • To find how many 1 cm squares fit in a 1 m² square, calculate 100 cm x 100 cm, resulting in 10,000 cm².
  • Converting 15.0 liters to milliliters requires multiplying by 1,000, resulting in 15,000 mL or 1.5 x 10^4 mL.
  • For cubic centimeters, 15.0 liters equals 15,000 cm³ since 1 L = 1,000 cm³.
  • To convert 15.0 liters to gallons, use the conversion factor 1 L = 0.264172 gallons, resulting in approximately 3.96 gallons.
  • Converting 15.0 liters to quarts involves multiplying by 1.05674, yielding approximately 15.9 quarts.
  • A ruler measuring a penny has 1 mm markings; the correct measurement for a penny's diameter is 19.1 mm, approximating the next digit.
  • Significant digits in 0.000012 are 2; in 8123 x 10^4, there are 4; and in 3127 seconds, there are 4 significant digits.
  • Exact numbers like 12 inches in a foot have unlimited significant digits, while rounded figures like the U.S. population of 331 million have 3 significant digits.

45:04

Calculating Significant Digits and Densities

  • To calculate significant digits, multiply 27.5 by 1.82, yielding 50.3, which rounds to 0.50 due to three significant digits.
  • For 2.29 * 10^6 divided by 6.7 * 10^4, the result is 34, limited to two significant digits.
  • Use the TI-30X II calculator's E button for exponential notation, entering values as 2.29 E6 divided by 6.7 E4.
  • Problem 49 involves calculating 2.1 * 10^3 divided by 5.39 * 10^4, resulting in 0.39 or 3.9 * 10^-1, with two significant digits.
  • In problem 51A, calculate 24.6681 * 2.38 plus 33258, yielding 39129, rounded to 391 with three significant digits.
  • For problem 51B, subtract 2.48 from 85.3, divide by 0.0059, resulting in 1.1 * 10^4, limited to two significant digits.
  • Problem 51C involves dividing 512 by 9867, adding 5.44, resulting in 5.96, rounded to three significant digits.
  • The density of a penny is calculated by dividing its mass (2.49 g) by its volume (0.349 cm³), yielding 7.13 g/cm³, not equal to copper's density of 8.96 g/cm³.
  • For glycerol, divide 4.10 * 10^3 g by 3.25 L, converting to g/cm³, resulting in a density of 1.26 g/cm³, with three significant digits.
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