9. A lump of gold sample is suspected to have a mass of 500g and is found to have a relative den of 5.2
Find what mass of gold is present in the sample
If the relative den of gold and aluminium are 19.3 and 2.6
g = gold mass
a = Al mass
p = gold volume
r = Al volume
g+a = 500 so a = 500 -g
500 / (p+r) = 5.2
g/p = 19.3 so p = g/19.3
a/r = 2.6 so r = a/2.6
500 / [ g/19.3 + a/2.6 ] = 5.2
500 / [ g/19.3 + (500-g)/2.6 ] = 5.2
solve for g
Good
Well, if your gold sample weighs 500g and has a relative density of 5.2, we can calculate the volume of the sample using the formula:
Volume = Mass / Relative Density
Volume = 500g / 5.2 = 96.15 cm³
Now, if the relative density of gold is 19.3, we can find the mass of gold in the sample by multiplying the volume by the relative density:
Mass of gold = Volume × Relative Density of Gold
Mass of gold = 96.15 cm³ × 19.3 = 1857.38 g
So, the mass of gold in the sample is approximately 1857.38 grams. I hope that answers your question.
To find the mass of gold present in the sample, we need to use the formula:
Mass = Volume x Density
Given the relative density (den) of gold is 19.3, and the mass of the sample is 500g, we can rearrange the formula as:
Volume = Mass / Density
Volume of gold = 500g / 19.3
Now, we need to find the volume of the gold in the sample.
Given the relative density (den) of gold is 19.3 and the relative density (den) of the sample is 5.2, we can use the equation:
Volume of gold / Volume of sample = Den of gold / Den of sample
Substituting the values, we get:
Volume of gold / Volume of sample = 19.3 / 5.2
Now we can rearrange the equation to solve for the volume of gold:
Volume of gold = (Volume of sample x Den of gold) / Den of sample
Plugging in the values, we have:
Volume of gold = (500g / 19.3) x 5.2
Now we can calculate the mass of gold:
Mass of gold = Volume of gold x Density of gold
Substituting the values, we get:
Mass of gold = (500g / 19.3) x 5.2 x 19.3
Therefore, the mass of gold present in the sample is (500g / 19.3) x 5.2 x 19.3.
To find the mass of gold present in the sample, we need to use the formula:
Mass = Relative Density x Volume
In this case, we are given the relative density of gold, which is 19.3, but we are not given the volume of the sample. However, we are given the mass of the sample, which is 500g.
We can use the formula for density to find the volume of the sample:
Density = Mass / Volume
Since density is defined as mass divided by volume, we can rearrange the formula to solve for volume:
Volume = Mass / Density
Now, substitute the given values into the formula:
Volume = 500g / 5.2
Volume ≈ 96.15 cm³ (rounded to two decimal places)
Now that we have the volume, we can find the mass of gold present in the sample:
Mass of Gold = Relative Density of Gold x Volume
Mass of Gold = 19.3 x 96.15 cm³
Mass of Gold ≈ 1855.20g (rounded to two decimal places)
Therefore, the mass of gold present in the sample is approximately 1855.20 grams.