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Chapter 1: Problem 80

What is the density of glass in \(\mathrm{g} / \mathrm{cm}^{3}\) if a sample weighing \(27.43 \mathrm{~g}\) has a volume of \(12.40 \mathrm{~cm}^{3} ?\)

Short Answer

Expert verified
The density of the glass is approximately 2.21 g/cm鲁.

Step by step solution

01

Identify the Formula for Density

Density is calculated using the formula: \( \text{Density} = \frac{\text{mass}}{\text{volume}} \). Here, the mass of the glass is 27.43 g, and the volume is 12.40 cm鲁.
02

Insert Values into the Formula

Substitute the given values into the density formula: \( \text{Density} = \frac{27.43 \, \text{g}}{12.40 \, \text{cm}^3} \).
03

Calculate the Density

Perform the division to calculate the density: \( \text{Density} = 2.2121 \ldots \approx 2.21 \, \text{g/cm}^3 \). Round to two decimal places for precision.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Mass and Volume
Mass and volume are fundamental concepts in scientific measurements, especially when calculating density. Mass refers to the amount of matter that is present in an object. It is often measured in grams (g) when dealing with smaller objects. The volume is the amount of space that an object occupies, typically measured in cubic centimeters (cm鲁) for solid objects.
  • Mass: It is independent of location and remains constant regardless of gravitational changes. For example, the mass of a glass sample is the same on Earth as it is on the Moon.
  • Volume: This can change depending on the state of the substance. Solids have a fixed volume, while liquids and gases can adjust based on the container they are in.
In our context, a glass sample weighing 27.43 grams occupies 12.40 cubic centimeters. Understanding these measurements helps to determine the density, a property that characterizes each material's compactness.
The Role of Scientific Measurement
Scientific measurements are crucial in experiments and studies because they provide accurate and objective data. In the context of calculating density, precise measurements of mass and volume are essential.
  • Precision: Ensuring that your equipment, such as weighing scales and measuring cylinders, are properly calibrated is vital for accurate measurements.
  • Significant Figures: These are important in expressing the precision of your measurement. They indicate the certainty of the measurement and include all known digits plus one estimated digit.
  • Rounding: When you calculate a quantity, like density, it's common to round the result to a certain number of significant figures, usually to match the precision of the initial measurements.
In the original exercise, the density calculation is rounded to two decimal places, reflecting the precision of both the mass and volume measurements given.
Navigating Unit Conversion
Unit conversion is often necessary in scientific calculations to ensure that units are consistent across different measurements. This process can help avoid confusion and errors.
  • Consistency: In the problem of determining density, mass is given in grams and volume in cubic centimeters, which is convenient because density in \(g/cm^3\) is a standard unit.
  • Conversion Factors: Sometimes, converting units involves using factors like 1000 mL = 1 L or 1 inch = 2.54 cm to convert between units. These are ratios that allow for the conversion without changing the value of the measurement.
  • Dimensional Analysis: This method is a systematic way to convert units using multiplication or division along with conversion factors, ensuring units cancel appropriately.
Luckily, in our exercise, the units were already provided in grams and cubic centimeters, making the calculation straightforward without needing any conversions.

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Most popular questions from this chapter

Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of \(-117.3^{\circ} \mathrm{C}\) and a boiling point of \(78.5^{\circ} \mathrm{C}\), but on your new scale calibrated in units of degrees ethanol, \({ }^{\circ} \mathrm{E}\), you define ethanol to melt at \(0{ }^{\circ} \mathrm{E}\) and boil at \(200^{\circ} \mathrm{E}\). (a) How does your ethanol degree compare in size with a Celsius degree? (b) How does an ethanol degree compare in size with a Fahrenheit degree? (c) What are the melting and boiling points of water on the ethanol scale? (d) What is normal human body temperature \(\left(98.6^{\circ} \mathrm{F}\right)\) on the ethanol scale? (e) If the outside thermometer reads \(130{ }^{\circ} \mathrm{E}\), how would you dress to go out?

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The melting point of table salt is \(1474^{\circ} \mathrm{F}\). What temperature is this on the Celsius and Kelvin scales?

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How many picograms are in \(1 \mathrm{mg} ?\) In \(35 \mathrm{ng}\) ?
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