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Union University Department of Physics

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Science Guys >August 2000

August 2000

How much does a gallon of gold weigh?

Science is very specific and has specific definitions for its terminology. In everyday layman’s language people may use the word weight and mass interchangeably, however in science there is a distinct difference. People who use the metric system people usually speak of mass, while people using the English system of measurement usually speak of weight. The two quantities mass and weight are directly related but not identical. Here on Earth the weight of an object is equal to the mass of the object times the acceleration due to Earth’s gravity, which is 9.8 m/s2 or 32 ft/s2.

To answer this month’s question, we must refer to a quantity called density. We can use either the English (weight) density or the metric (mass) density to answer the question. Density is a quantity that relates the amount of material present (mass or weight) to the amount of space (volume) it takes up. (Density tells us how much stuff is packed into how much space.) In the English system we use the weight of the material, while in the metric system the mass of the material is used. The exact relationship is density = mass or weight divided by volume.

Different materials have different densities. For example, the mass density of gold is 19.3 g/cc, lead is 11.4 g/cc, copper is 9.0 g/cc, aluminum is 2.7 g/cc, water is 1.0 g/cc (1g/cc = 1 gram per cubic centimeter). If we want the density in English units we could use 11.1 oz/cubic inch as the density of gold.

A gallon contains 3785 cubic centimeters or 231 cubic inches. Since each cc has a mass of 19.3 g, a gallon of gold has a mass of 73051 g (3785 cc x 19.3 g/cc). A pound contains 454 g of mass so 73501 g divided by 454 g/lb gives us the weight in pounds, 160.9 pounds. Thus a gallon of gold weighs 160.9 pounds. The old cowboy who robbed a stagecoach could not just throw a saddlebag of gold over his shoulder and ride off into the sunset. Gold is much heavier than lead. It is very dense.

Another rather simple way to think of this is that if the density of water is 1 g/cc then the density of gold is 19.3 times greater than water. Water weighs about 8.3 pounds per gallon. Therefore gold weighs 19.3 times as much or (19.3 x 8.3 lb) about 160 pounds per gallon.

Although gold has a density 19.3 times greater than water and is one of the most dense substances on Earth, there are substances with far more amazing densities. The core of our own Sun has a calculated density 115 times that of water (nearly 6 times denser than gold) yet it is not a solid! Neutron stars are thought to be composed of a material so dense that a single teaspoonful would weigh one billion tons if brought to Earth!

The gold calculations above have assumed we are using everyday measuring units. Technically in the "gold" business a different unit of measure is used and a "gold" pound is taken as 12 ounces. This gives rise to the old riddle - which weighs more a pound of gold or a pound of feathers? Since gold is usually measured in the troy system and only weighs 12 ounces, the pound of feathers weighs more.

(Densities are readily available in physical science books and on the web. One such resource is www.webelements.com. This site provides an abundance of physical-chemical data for each element.)