Calculating Gold Mass in a 12.08 kg Quartz-Gold Rock

In summary, the rock hound found a solid rock with a mass of 12.08 kg and a volume of 3.909×10-3 m^3. The rock contains only quartz and gold, with the densities of 2660 kg/m^3 and 19300 kg/m^3 respectively. To find the mass of gold contained in the rock, the density of gold must be multiplied by the volume of the rock and then divided by the total density of the rock.
  • #1
yuvlevental
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A rock hound finds a solid rock that contains only quartz and gold. The rock has a mass of 12.08 kg and a volume of 3.909×10-3 m^3. What is the mass of the gold contained in the rock?

Density of gold: 19300 kg/m^3
Density of quarts: 2660 kg/m^3
 
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  • #2
yuvlevental said:
A rock hound finds a solid rock that contains only quartz and gold. The rock has a mass of 12.08 kg and a volume of 3.909×10-3 m^3. What is the mass of the gold contained in the rock?

Density of gold: 19300 kg/m^3
Density of quarts: 2660 kg/m^3
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  • #3


To calculate the mass of gold in the rock, we first need to determine the volume of gold present in the rock. This can be done by subtracting the volume of quartz from the total volume of the rock.

Volume of quartz = density of quartz x mass of quartz / density of rock

= (2660 kg/m^3 x 12.08 kg) / (19300 kg/m^3)

= 1.668 x 10^-3 m^3

Volume of gold = Total volume of rock - Volume of quartz

= 3.909 x 10^-3 m^3 - 1.668 x 10^-3 m^3

= 2.241 x 10^-3 m^3

Now, using the density of gold, we can calculate the mass of gold present in the rock:

Mass of gold = density of gold x volume of gold

= 19300 kg/m^3 x 2.241 x 10^-3 m^3

= 43.59 kg

Therefore, the mass of gold contained in the rock is approximately 43.59 kg. This information can be useful for further analysis and understanding of the composition and value of the rock.
 

Related to Calculating Gold Mass in a 12.08 kg Quartz-Gold Rock

1. How do you calculate the mass of gold in a quartz-gold rock?

To calculate the mass of gold in a quartz-gold rock, you will need to use the density of gold and the mass of the entire rock. The density of gold is 19.3 g/cm3. First, measure the volume of the rock by submerging it in a graduated cylinder filled with water and recording the difference in water level. Then, multiply the volume by the density of gold to get the mass of gold in grams. Finally, convert the mass to kilograms by dividing by 1000.

2. What is the equation for calculating gold mass in a 12.08 kg quartz-gold rock?

The equation for calculating gold mass in a 12.08 kg quartz-gold rock is: (density of gold x volume of rock) / 1000 = mass of gold in kilograms.

3. Can you use a scale to measure the mass of gold in a quartz-gold rock?

Yes, you can use a scale to measure the mass of gold in a quartz-gold rock. However, a scale may not be accurate enough for precise measurements and it is recommended to use the density method described above.

4. Why is it important to calculate the mass of gold in a quartz-gold rock?

Calculating the mass of gold in a quartz-gold rock is important for several reasons. It can help determine the value of the rock, as gold is a valuable metal. It can also provide important information about the formation and composition of the rock, which can be useful for geological studies. Additionally, knowing the mass of gold in a rock can help with mining and extraction processes.

5. Are there any other factors that can affect the accuracy of calculating gold mass in a quartz-gold rock?

Yes, there are several other factors that can affect the accuracy of calculating gold mass in a quartz-gold rock. These include variations in the density of gold, impurities in the rock, and errors in measuring the volume of the rock. It is important to take these factors into consideration and use multiple methods for calculating the mass of gold to ensure accuracy.

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