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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

The following statements pertain to the development of the theory of the structure of DNA. Match the statement with the appropriate step (observation, hypothesis, experiment designed to test hypothesis) in the scientific method. (a) Two strands of DNA wind around one another in a helical structure. (b) In a sample of DNA, there are equal amounts of the bases \(\mathrm{A}\) and \(\mathrm{T}\) and equal amounts of the bases \(\mathrm{C}\) and \(\mathrm{G}\). (c) Direct X-rays at a sample of crystallized DNA and interpret the diffraction pattern for structural information.

The element gallium (Ga) has the second largest liquid range of any element, melting at \(29.78{ }^{\circ} \mathrm{C}\) and boiling at \(2204{ }^{\circ} \mathrm{C}\) at atmospheric pressure. (a) What is the density of gallium in \(\mathrm{g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\) if a 1 in. cube has a mass of \(0.2133 \mathrm{lb} ?\) (b) Assume that you construct a thermometer using gallium as the fluid instead of mercury, and that you define the melting point of gallium as \(0{ }^{\circ} \mathrm{G}\) and the boiling point of gallium as \(1000^{\circ} \mathrm{G}\). What is the melting point of sodium chloride \(\left(801{ }^{\circ} \mathrm{C}\right)\) on the gallium scale?

Vinaigrette salad dressing consists mainly of oil and vinegar. The density of olive oil is \(0.918 \mathrm{~g} / \mathrm{cm}^{3}\), the density of vinegar is \(1.006 \mathrm{~g} / \mathrm{cm}^{3}\), and the two do not mix. If a certain mixture of olive oil and vinegar has a total mass of \(397.8 \mathrm{~g}\) and a total volume of \(422.8 \mathrm{~cm}^{3}\), what is the volume of oil and what is the volume of vinegar in the mixture?

Label the following statements as quantitative or qualitative observations. (a) An object weighs less on the moon than on Earth. (b) An object that weighs 50 pounds on Earth only weighs \(8.3\) pounds on the moon. (c) The freezing point of water is cold. (d) The freezing point of water is \(0{ }^{\circ} \mathrm{C}\).

Platinum is an expensive and rare metal used in catalytic converters and other industrial applications. Much research has been devoted to maximizing reactive properties of other metals by shrinking them to nanoparticles in the hope that someday they will be an efficient and economic alternative to platinum. (a) Explain why changing the size of a metal particle influences its reactivity. (b) What is the economic benefit of using small particles? (c) What properties other than reactivity might you expect to change as the size of particle approaches the nanoscale?
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