A lump of gold is suspected to contain some -quantity of zinc. If the gold sample has a mass of 500g and found to have a density of 5*2g/cm^ 2 what mass of gold is present of density of gold and zing are 19*3g/cm 2*6g/cm^ 3 respectively?
Not sure what 5*2g/cm^2 is supposed to mean. I suspect you meant 5.2, since the density of gold is 19.3
So, if there are x grams of gold in the alloy, then
19.3x + 2.6(500-x) = 5.2*500
x/19.3+(500-x)/2.6=500/5.2
=288.9
To find the mass of gold present in the lump, we need to determine the volume of the gold in the sample.
Given:
- Mass of the gold sample = 500g
- Density of gold = 19.3g/cm^3
- Density of zinc = 6g/cm^3
First, let's find the total volume of the sample. We can use the formula:
Volume = Mass / Density
Volume = 500g / (5.2g/cm^2) [Note: We need to convert g/cm^2 to g/cm^3 by dividing by 100]
Volume = 500g / (5.2g/cm^3) / 100
Volume = 9.615 cm^3
Now, let's find the volume of the zinc in the sample. We know the density of zinc is 6g/cm^3, so we can use the formula:
Volume of zinc = Mass of zinc / Density of zinc
We will assume that the entire volume of the zinc is in the form of a perfect cube.
Since the density of zinc is different from that of gold, we need to determine the percentage of the sample that is zinc. To do this, we'll set up a proportion:
(zinc volume) / (total volume) = (density of zinc) / (density of gold)
(zinc volume) / 9.615 cm^3 = 6g/cm^3 / 19.3g/cm^3
(zinc volume) = (9.615 cm^3) * (6g/cm^3 / 19.3g/cm^3)
(zinc volume) = 9.615 cm^3 * 0.31088
(zinc volume) = 2.985 cm^3
Since the volume of a cube is equal to the edge of the cube cubed, we can find the edge length of the zinc cube:
Edge length of the zinc cube = volume^(1/3)
Edge length of the zinc cube = (2.985 cm^3)^(1/3)
Edge length of the zinc cube ≈ 1.43 cm
Now, let's find the mass of the gold in the sample:
Volume of gold = Total volume - Volume of zinc
Volume of gold = 9.615 cm^3 - 2.985 cm^3
Volume of gold ≈ 6.63 cm^3
Mass of gold = Volume of gold * Density of gold
Mass of gold = 6.63 cm^3 * 19.3g/cm^3
Mass of gold ≈ 128g
Therefore, the mass of gold present in the sample is approximately 128 grams.
To find the mass of gold present in the sample, you need to know the density of the gold and zinc, as well as the volume of the gold sample.
Density is defined as mass divided by volume. In this case, we know the density of gold is 19.3 g/cm³ and the density of zinc is 6 g/cm³.
First, let's calculate the volume of the gold sample. We can use the formula:
Volume = mass / density
Given:
Mass of gold sample = 500 g
Density of gold = 19.3 g/cm³
Volume of gold sample = 500 g / 19.3 g/cm³ = 25.90 cm³
Now, let's find the mass of gold in the sample using the volume and densities of gold and zinc.
Let's assume the mass of gold in the sample (without zinc) is 'x' grams.
Since the total mass of the sample is 500g, we have the equation:
x + mass of zinc = 500 g
Now, let's calculate the mass of zinc in the sample using the volume and density of zinc:
Volume of zinc = Volume of gold sample - Volume of gold
Given:
Density of zinc = 6 g/cm³
Volume of gold = 25.90 cm³
Volume of zinc = 25.90 cm³ - Volume of gold
Now, let's calculate the mass of zinc:
Mass of zinc = Density of zinc * Volume of zinc
Given:
Density of zinc = 6 g/cm³
Volume of zinc = 25.90 cm³ - Volume of gold
Mass of zinc = 6 g/cm³ * (25.90 cm³ - Volume of gold)
Mass of zinc = (6 g/cm³ * 25.90 cm³) - (6 g/cm³ * Volume of gold)
Since we have x + mass of zinc = 500 g and x is the mass of gold, we can substitute the expression for mass of zinc into the equation:
x + (6 g/cm³ * 25.90 cm³) - (6 g/cm³ * Volume of gold) = 500 g
Now we can solve this equation to find the mass of gold (x):
x - 6g/cm³ * Volume of gold = 500 g - (6 g/cm³ * 25.90 cm³)
x - 6g/cm³ * Volume of gold = 500 g - (154.8 g)
x - 6g/cm³ * Volume of gold = 345.2 g
Finally, you can use the volume of the gold sample to get the mass of gold.
Volume = mass / density
Volume of gold = x / 19.3 g/cm³
Now, you can substitute the expression for the volume of gold into the equation:
x - 6g/cm³ * (x / 19.3 g/cm³) = 345.2 g
Now, solve this equation to find the mass of gold (x).