A gold prospector finds a solid rock that is composed solely of quartz and gold. The mass and volume of the rock are, respectively, 13.3 kg and 3.56 × 10-3 m3. The density of gold is 19 300 kg/m3, and the density of quartz is 2660 kg/m3. Find the mass of the gold in the rock.
mass gold+mass quartz=13.3
massgold/densitygold+massquartz/densityquartz=3.56E-3
you have two equations, two unknowns, solve for mass gold
To find the mass of the gold in the rock, we need to determine the volume of gold in the rock and then use the density of gold to calculate its mass.
First, let's calculate the volume of gold in the rock. We know the total volume of the rock is 3.56 × 10-3 m3. Since the rock is composed solely of quartz and gold, the volume of quartz and gold combined is equal to the total volume of the rock.
Let's denote the volume of gold as Vg and the volume of quartz as Vq. Since the rock is composed solely of quartz and gold, we have:
Vg + Vq = 3.56 × 10-3 m3
Now, let's calculate the volume of quartz in the rock. Since we know the total mass and volume of the rock, we can calculate the mass and volume of the quartz using their respective densities.
The density of quartz is given as 2660 kg/m3. We can calculate the mass of quartz (Mq) using the mass equation:
Mq = density × volume = 2660 kg/m3 × Vq
Since the mass of the rock is 13.3 kg, and the mass of quartz is Mq, we have:
Mass of quartz + Mass of gold = Mass of the rock
Mq + Mg = 13.3 kg
Now, let's substitute the values of Mq and Vq into the equation:
Mq + Mg = 13.3 kg
2660 kg/m3 × Vq + Mg = 13.3 kg
We have two equations with two unknowns (Mg and Vq). By substituting the value of Vq from the first equation into the second equation, we can solve for Mg:
2660 kg/m3 × (3.56 × 10-3 m3 - Vg) + Mg = 13.3 kg
Now, let's substitute the values given in the problem. The density of gold is 19,300 kg/m3, and the total volume of the rock is 3.56 × 10-3 m3. We can solve for Vg using the equation above.
After solving for Vg, we can calculate the mass of the gold (Mg) using the density of gold:
Mg = density of gold × Vg
So, this is how we can find the mass of the gold in the rock.
To find the mass of the gold in the rock, we need to determine the volume occupied by the gold.
Step 1: Calculate the volume occupied by quartz:
The volume of the rock is given as 3.56 × 10^-3 m^3. Since the rock is composed solely of quartz and gold, the volume occupied by quartz is equal to the volume of the rock itself.
Volume of quartz = 3.56 × 10^-3 m^3
Step 2: Calculate the mass of quartz:
The density of quartz is given as 2660 kg/m^3. We can use the density formula to calculate the mass of quartz.
Density = Mass / Volume
Rearranging the formula, we get:
Mass = Density x Volume
Mass of quartz = 2660 kg/m^3 x 3.56 × 10^-3 m^3
Step 3: Calculate the mass of the gold:
The mass of the rock is given as 13.3 kg. We can subtract the mass of quartz from the total mass to find the mass of the gold.
Mass of gold = Mass of rock - Mass of quartz
Mass of gold = 13.3 kg - Mass of quartz
Finally, we substitute the values into the equation to find the mass of the gold.