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Chapter 2: Problem 35

Which is denser, a 200 pound block of lead or a \(0.1-\mathrm{g}\) piece of gold?

Short Answer

Expert verified
The 0.1g piece of gold is denser than the 200-pound block of lead, with a density of approximately 19.33 g/cm³ for gold and 11.34 g/cm³ for lead.

Step by step solution

01

Convert mass to a single unit

Before proceeding, we need to convert the mass of the lead to grams since the mass of the gold is given in grams. The conversion rate between pounds and grams is 1 lbs = 453.592 grams. \(200\, lbs = 200 \times 453.592\, g = 90718.4\, g\) Now we have the mass of lead and gold in grams: Lead mass = 90718.4 g Gold mass = 0.1 g
02

Find the volume of each substance

In order to calculate the volume of each substance, we need to know their mass and density. The density of lead is 11.34 g/cm³, and the density of gold is 19.32 g/cm³. We can use the mass and density to find the volume using the formula: Volume = mass/density For lead: Volume = \( \frac{90718.4\, g}{11.34\, g/cm³} \) For gold: Volume = \( \frac{0.1\, g}{19.32\, g/cm³} \)
03

Calculate the volume and density of each substance

Now we will calculate the volume and density of each substance. Lead volume = \( \frac{90718.4\, g}{11.34\, g/cm³} = 8000\, cm³ \) Gold volume = \( \frac{0.1\, g}{19.32\, g/cm³} \approx 0.00517\, cm³ \) Now, we will use the mass and volume to calculate the density of each substance. Lead density = \( \frac{90718.4\, g}{8000\, cm³} = 11.34\, g/cm³ \) Gold density = \( \frac{0.1\, g}{0.00517\, cm³} \approx 19.33\, g/cm³ \)
04

Compare the densities

We can now compare the densities of lead and gold. As we can see, the density of gold is 19.33 g/cm³, and the density of lead is 11.34 g/cm³. Since 19.33 g/cm³ > 11.34 g/cm³, we can conclude that the 0.1g piece of gold is denser than the 200-pound block of lead.

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Most popular questions from this chapter

The density of water at \(4.00^{\circ} \mathrm{C}\) is \(1.00 \mathrm{~g} / \mathrm{mL}\). The density of ice at \(0{ }^{\circ} \mathrm{C}\) is \(0.917 \mathrm{~g} / \mathrm{mL}\). Water is different from most other substances in that the solid phase (ice) is less dense than the liquid phase. Explain why this characteristic makes ice fishing possible.

How many joules of heat energy would it take to raise the temperature of \(2.00\) pounds of iron from \(30.0^{\circ} \mathrm{C}\) to \(90.0^{\circ} \mathrm{C} ?[453.6 \mathrm{~g}=1\) pound \(]\)

Solve the equation \(y=z-x\) for \(x\).

At \(25^{\circ} \mathrm{C}\), air has a density of \(1.3 \times 10^{-3} \mathrm{~g} / \mathrm{mL}\). What is this density in (a) kilograms per liter and (b) pounds per gallon?

If 1 U.S. dollar is worth \(0.690\) English pounds, how many U.S. dollars are needed to purchase an item that costs 350 pounds?
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