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Chapter 1: Problem 59

Calculate the mass of each of the following: (a) a sphere of gold with a radius of \(10.0 \mathrm{~cm}\) [ the volume of a sphere with a radius \(r\) is \(V=(4 / 3) \pi r^{3} ;\) the density of gold \(\left.=19.3 \mathrm{~g} / \mathrm{cm}^{3}\right],\) (b) a cube of platinum of edge length \(0.040 \mathrm{~mm}\) (the density of platinum \(=\) \(\left.21.4 \mathrm{~g} / \mathrm{cm}^{3}\right),\) (c) \(50.0 \mathrm{~mL}\) of ethanol (the density of cthanol \(=0.798 \mathrm{~g} / \mathrm{mL}\) ).

Short Answer

Expert verified
The mass of the gold sphere is approximately 80385 g. The mass of the platinum cube is approximately 0.014 g. The mass of the 50.0 mL ethanol is approximately 39.9 g.

Step by step solution

01

Calculate the volume of the gold sphere

The volume formula for a sphere is \(V=(4 / 3) \pi r^{3}\). Substitute \(10.0 cm\) for \(r\), and calculate the volume.
02

Calculate the mass of the gold sphere

Density equals mass divided by volume. The mass can therefore be calculated by rearranging the equation to be mass = density * volume. Substitute the volume calculated in Step 1 and the given density of gold, \(19.3 g/cm^{3}\), into the equation to find the mass.
03

Calculate the volume of the platinum cube

The volume of a cube is calculated by the formula \(V = a^{3}\), where \(a\) is the length of an edge of the cube. Substitute \(.040 mm\) for \(a\), noting that you need to convert from \(mm\) to \(cm\) first, as 1 \(mm\) = .1 \(cm\).
04

Calculate the mass of the platinum cube

Again, use the rearranged density formula mass = density * volume to find the mass. Substitute the volume calculated in Step 3 and the given density of platinum, \(21.4 g/cm^{3}\), into the equation to find the mass.
05

Calculate the mass of the 50.0 mL of ethanol

Because the volume of the ethanol is given in \(mL\) and the density in \(g/mL\), you can directly apply the rearranged density formula mass = density * volume to find the mass. Substitute \(50.0 mL\) for the volume and the given density of ethanol, \(0.798 g/mL\), into the equation to find the mass.

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Most popular questions from this chapter

The "normal" lead content in human blood is about 0.40 part per million (that is, \(0.40 \mathrm{~g}\) of lead per million grams of blood). A value of 0.80 part per million (ppm) is considered to be dangerous. How many grams of lead are contained in \(6.0 \times 10^{3} \mathrm{~g}\) of blood (the amount in an average adult) if the lead content is \(0.62 \mathrm{ppm} ?\)

A bank teller is asked to assemble "one-dollar" sets of coins for his clients. Each set is made of three quarters, one nickel, and two dimes. The masses of the coins are: quarter: 5.645 g; nickel: \(4.967 \mathrm{~g}\) dime: 2.316 g. What is the maximum number of sets that can be assembled from \(33.871 \mathrm{~kg}\) of quarters, \(10.432 \mathrm{~kg}\) of nickels, and \(7.990 \mathrm{~kg}\) of dimes? What is the total mass (in g) of the assembled sets of coins?

How many significant figures are there in each of the following? (a) \(0.006 \mathrm{~L},\) (b) \(0.0605 \mathrm{dm},\) (c) \(60.5 \mathrm{mg}\), (d) \(605.5 \mathrm{~cm}^{2}\) (e) \(960 \times 10^{-3} \mathrm{~g},(\mathrm{f}) 6 \mathrm{~kg},(\mathrm{~g}) 60 \mathrm{~m}\)

Explain how the distances between particles typically change with different states of matter.

Convert the following temperatures to degrees Celsius: (a) \(77 \mathrm{~K}\), the boiling point of liguid nitrogen, (b) \(4.2 \mathrm{~K},\) the boiling point of liquid helium, (c) \(601 \mathrm{~K},\) the melting point of lead.
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