Ch.2 - Atoms, Molecules, and Ions

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.2 - Atoms, Molecules, and Ions

Problem 91b

Chapter 2, Problem 91b

(b) Using the mass of the proton from Table 2.1 and assuming its diameter is 1.0 * 10-15 m, calculate the density of a proton in g>cm3.

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Identify the mass of a proton from Table 2.1, which is approximately 1.67 \(\times\) 10^{-27} \(\text{ kg}\).

Convert the mass of the proton from kilograms to grams by using the conversion factor: 1 \(\text{ kg}\) = 1000 \(\text{ g}\).

Assume the proton is spherical and use the formula for the volume of a sphere: V = \(\frac{4}{3}\) \(\pi\) r^3, where r is the radius of the proton.

Calculate the radius of the proton by dividing the given diameter (1.0 \(\times\) 10^{-15} \(\text{ m}\)) by 2.

Convert the volume from cubic meters to cubic centimeters using the conversion factor: 1 \(\text{ m}\)^3 = 10^6 \(\text{ cm}\)^3, and then calculate the density using the formula: \(\text{Density}\) = \(\frac{\text{mass}\)}{\(\text{volume}\)}.

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Key Concepts

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

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³) in chemistry. It provides a measure of how much matter is contained in a given volume. To calculate density, one can use the formula: density = mass/volume. Understanding this concept is crucial for determining the density of a proton based on its mass and volume.

Mass of a Proton

The mass of a proton is a fundamental constant in physics and chemistry, approximately 1.67 x 10^-24 grams. This value is essential for calculations involving atomic and molecular masses. In the context of the question, knowing the mass of the proton allows for the calculation of its density when combined with its volume.

Volume of a Sphere

The volume of a sphere is calculated using the formula V = (4/3)πr³, where r is the radius. In this case, the diameter of the proton is given, so the radius can be determined by dividing the diameter by two. This volume is necessary to find the density of the proton, as it provides the space occupied by the mass of the proton.

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Identify the element represented by each of the following symbols and give the number of protons and neutrons in each: (a) ⁷⁴₃₃X

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(a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the atom is taken up by the nucleus?

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Identify the element represented by each of the following symbols and give the number of protons and neutrons in each: (b) ¹²⁷₅₃X (c) ⁸⁶₃₆X (d) ⁶⁷₃₀X

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