A gold prospector finds a solid rock that is composed solelyof quartz and gold.

Question

A gold prospector finds a solid rock that is composed solelyof quartz and gold. The mass and volume of the rock are,respectively, 11.4 kg and 4.20 x 10-3m3. The density of gold is 19 300 kg/m3, andthe density of quartz is 2660 kg/m3. Find the mass ofthe gold in the rock. Please provide steps and final result... I've been trying towork this problem and just can't seem to get it. Thanks in advance! A gold prospector finds a solid rock that is composed solelyof quartz and gold. The mass and volume of the rock are,respectively, 11.4 kg and 4.20 x 10-3m3. The density of gold is 19 300 kg/m3, andthe density of quartz is 2660 kg/m3. Find the mass ofthe gold in the rock. Please provide steps and final result... I've been trying towork this problem and just can't seem to get it. Thanks in advance!

Explanation / Answer

    Mass of the rock, M = 11.4 kg     Volume of the rock, V = 4.2 X 10 -3m^3     Density of gold, 1 = 19300 kg/m^3     Density of quartz, 2 = 2660 kg/m^3     Let     Volume of gold, V1 = x     Volume of quartz, V2 = V - x     Mass of the rock = Mass of Gold + Mass ofquartz                         M = 1 V1 + 2 V2                       11.4 = 19300 x + 2660 ( 4.2 X 10 -3 - x )                        11.4 = 19300 x + 11.172 - 2660 x                     16640 x = 0.228                          Volume of the gold, x = 1.37 X 10 -5m^3     Mass of the gold = Density of gold * Volume ofgold                              = 1 x                              = 19300 * 1.37 X 10 -5                              = 0.2644 kg

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