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Chapter 1: Problem 88

Osmium is one of the densest elements known. What is its density if 2.72 g has a volume of \(0.121 \mathrm{cm}^{3} ?\)

Short Answer

Expert verified
The density of osmium is approximately \(22.48 \text{ g/cm}^{3} \).

Step by step solution

01

Understand the concept of density

Density is defined as the mass per unit volume of an object. It can be calculated using the formula: density \( d = \frac{m}{V} \) where \( m \) is the mass and \( V \) is the volume.
02

Identify the known values

From the problem, we know the mass \( m = 2.72 \text{ g} \) and the volume \( V = 0.121 \mathrm{cm}^{3} \).
03

Insert the known values into the formula

Substitute the values of mass and volume into the density formula: \( d = \frac{2.72 \text{ g}}{0.121 \mathrm{cm}^{3}} \).
04

Calculate the density

Perform the division to obtain the density of osmium: \( d \approx \frac{2.72}{0.121} \text{ g/cm}^{3} \).
05

Report the final answer

Complete the calculation to find the density to an appropriate number of significant figures: \( d \approx 22.48 \text{ g/cm}^{3} \).

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Key Concepts

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

Density Formula
Density is a fundamental concept in science, describing how much 'stuff' is packed into a certain space. To calculate it, the density formula \( d = \frac{m}{V} \) is essential, where \( d \) is density, \( m \) is mass, and \( V \) is volume.

Understanding this formula is crucial because it tells you how the mass of a substance is distributed within its volume. For example, osmium's density is high because a small volume contains a lot of mass. That's why, with a mass of 2.72 grams in a volume of just 0.121 cubic centimeters, osmium is considered one of the densest elements.
Mass and Volume
Mass and volume are the two critical components needed to calculate the density of an object. Mass is a measure of the amount of matter in an object and is typically measured in grams (g) or kilograms (kg). Volume is the amount of space that an object occupies and is commonly measured in cubic centimeters (\(\mathrm{cm}^{3}\)) or liters (L).

When working with these quantities, it's essential to use the correct units and to convert between units if necessary. For the osmium example, the mass provided is 2.72 g, and the volume is 0.121 \(\mathrm{cm}^{3}\), already tailored for direct use in the density formula without the need for conversion.
Significant Figures
Significant figures are a way of indicating the precision of a measurement. They include all the certain digits in a number plus one uncertain or estimated digit.

When calculating the density of osmium, we must consider significant figures. Since 2.72 has three significant figures and 0.121 has three as well, our calculation for density should also reflect three significant figures. This leads us to report the final density of osmium as approximately 22.5 g/cm³ instead of 22.48 g/cm³, after rounding to three significant digits. This ensures our answer's precision matches the precision of the given data.

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Most popular questions from this chapter

Explain how you could experimentally determine whether the outside temperature is higher or lower than \(0^{\circ}\) \(\left(32^{\circ} \mathrm{F}\right)\)without using a thermometer.

How many significant figures are contained in each of the following measurements? (a) 38.7 g (b) \(2 \times 10^{18} \mathrm{m}\) (c) 3,486,002 kg (d) \(9.74150 \times 10^{-4} \mathrm{J}\) (e) \(0.0613 \mathrm{cm}^{3}\) (f) \(17.0 \mathrm{kg}\) (g) 0.01400 g/mL

A long ton is defined as exactly 2240 lb. What is this mass in kilograms?

Round off each of the following numbers to two significant figures: (a) 0.436 (b) 9.000 (c) 27.2 (d) 135 (e) \(1.497 \times 10^{-3}\) (f) 0.445

Why is an object's mass, rather than its weight, used to indicate the amount of matter it contains?
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