Ch.1 - Introduction: Matter, Energy, and Measurement

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 57d

Chapter 1, Problem 57d

(d) Bamboo can grow up to 60.0 cm/day. Convert this growth rate into inches per hour.

Verified step by step guidance

Identify the conversion factors needed: 1 inch = 2.54 cm and 1 day = 24 hours.

Start with the given growth rate: 60.0 cm/day.

Convert centimeters to inches using the conversion factor: \( \frac{1 \text{ inch}}{2.54 \text{ cm}} \).

Convert days to hours using the conversion factor: \( \frac{1 \text{ day}}{24 \text{ hours}} \).

Combine the conversions to find the growth rate in inches per hour: \( 60.0 \text{ cm/day} \times \frac{1 \text{ inch}}{2.54 \text{ cm}} \times \frac{1 \text{ day}}{24 \text{ hours}} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. In this case, we need to convert centimeters to inches and days to hours. Understanding the conversion factors, such as 1 inch equals 2.54 centimeters and 1 day equals 24 hours, is essential for accurate calculations.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one unit of measurement to another by multiplying by conversion factors. This method ensures that units cancel appropriately, leading to the desired unit in the final answer. It is particularly useful in problems involving multiple unit conversions, as seen in this question.

Rate of Growth

The rate of growth refers to how quickly a quantity increases over time. In this context, bamboo's growth rate is given in centimeters per day, which needs to be expressed in inches per hour. Understanding how to manipulate these rates is crucial for solving problems related to growth and time.

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(d) An individual suffering from a high cholesterol level in her blood has 242 mg of cholesterol per 100 mL of blood. If the total blood volume of the individual is 5.2 L, how many grams of total blood cholesterol does the individual's body contain?

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(a) The speed of light in a vacuum is 2.998×10⁸ m/s. Calculate its speed in miles per hour.

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