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Chapter 1: Problem 83

A thief plans to steal a cylindrical platinum medal with a radius of $2.3 \mathrm{~cm}\( and a thickness of \)0.8 \mathrm{~cm}$ from a jewellery store. If the platinum has a density of \(21.45 \mathrm{~g} / \mathrm{cm}^{3},\) what is the mass of the medal in \(\mathrm{kg} ?\) [The volume of a cylinder is \(\left.V=\pi r^{2} h .\right]\)

Short Answer

Expert verified
The mass of the platinum medal is approximately \(0.28615 \, \mathrm{kg}\).

Step by step solution

01

Identify the given measurements

We are provided with the following measurements: - The radius of the cylindrical medal, \(r = 2.3 \, \text{cm}\) - The thickness (or height) of the medal, \(h = 0.8 \, \text{cm}\) - The density of platinum, \(d = 21.45 \, \frac{\text{g}}{\text{cm}^3}\)
02

Calculate the volume of the medal

We can find the volume of the cylindrical medal using the formula: \[V = \pi r^2 h\] Substitute the given values of radius and height into the formula: \[V = \pi (2.3)^2 (0.8)\] Now, compute the volume of the medal: \[V \approx 13.34 \, \text{cm}^3\]
03

Find the mass of the medal using the density formula

We know that the density, \(d\), is defined as the mass, \(m\), divided by the volume, \(V\). So we can find the mass using the formula: \[m = d V\] Substitute the given density and calculated volume into the formula: \[m = 21.45 (13.34)\] Now, compute the mass of the medal: \[m \approx 286.15 \, \text{g}\]
04

Convert the mass from grams to kilograms

To convert the mass of the medal from grams to kilograms, divide the mass in grams by 1,000: \[m_{\text{kg}} = \frac{286.15}{1,000}\] \[m_{\text{kg}} = 0.28615 \, \text{kg}\] So, the mass of the platinum medal is approximately \(0.28615 \, \mathrm{kg}\).

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Most popular questions from this chapter

In the process of attempting to characterize a substance, a chemist makes the following observations: The substance is a silvery white, lustrous metal. It melts at \(649^{\circ} \mathrm{C}\) and boils at \(1105^{\circ} \mathrm{C}\). Its density at \(20^{\circ} \mathrm{C}\) is \(1.738 \mathrm{~g} / \mathrm{cm}^{3}\). The substance burns in air, producing an intense white light. It reacts with chlorine to give a brittle white solid. The substance can be pounded into thin sheets or drawn into wires. It is a good conductor of electricity. Which of these characteristics are physical properties, and which are chemical properties?

Indicate which of the following are exact numbers: (a) the mass of a 945-mL can of coffee, \((\mathbf{b})\) the number of students in your chemistry class, \((\mathbf{c})\) the temperature of the surface of the Sun, \((\mathbf{d})\) the mass of a postage stamp, \((\mathbf{e})\) the number of milliliters in a cubic meter of water, (f) the average height of NBA basketball players.

Classify each of the following as a pure substance, a solution, or a heterogeneous mixture: \((\mathbf{a})\) a leaf, \((\mathbf{b})\) a 999 gold bar, (c) stainless steel.

Convert the following expressions into exponential notation: (a) 3 terameters \((\mathrm{tm})\) (b) 2.5 femtoseconds (fs) (c) 57 micrometers \((\mu m)\) (d) 8.3 megagrams (mg).

A silvery metal is put inside a beaker of water. Bubbles form on the surface of the metal and it dissolves gradually. (a) Is this an example of a chemical or a physical change? (b) Do you expect the remaining solution to be a pure substance of a mixture?
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