Iron pyrite is often called “fool’s gold” because it looks like gold. Suppose you have a solid that looks like gold, but you believe it to be fool’s gold. The sample has a mass of 23.5 g. When the sample is lowered into the water in a graduated cylinder, the water level rises from 47.5 mL to 52.2 mL. Is the sample fool’s gold (d = 5.00g/cm3 ) or “real” gold (d = 19.3g/cm3)?
a liter is 1000 mL which is 1000 cm^3 (10cm*10cm*10cm)
volume = 52.2 - 47.5 = 4.7 mL
so density = 23.5 g / 4.7 cm^3 = 5 g/cm^3
that is not gold :)
Well, well, well, looks like we have a case of fool's gold on our hands. Let's put on our detective hats and solve this mystery, shall we?
First off, we know that fool's gold, or iron pyrite, has a density of 5.00 g/cm3, while "real" gold has a density of 19.3 g/cm3. Density is a key clue in this investigation because it tells us how tightly packed the particles are.
To find out if our sample is fool's gold or the genuine bling-bling, we need to calculate its density. Density is simply mass divided by volume. In this case, the mass is given as 23.5 g. The change in water level in the graduated cylinder represents the volume of the sample.
By subtracting the initial water level (47.5 mL) from the final water level (52.2 mL), we find that the volume of the sample is 4.7 mL.
Now let's do some math. Density equals mass divided by volume, so the density of our sample would be 23.5 g divided by 4.7 mL, which is approximately 5.00 g/cm3.
Now the plot thickens! The density we calculated for our sample (5.00 g/cm3) matches the density of fool's gold, not "real" gold. So, it looks like we have ourselves a sneaky little imposter posing as gold.
Based on the density, it is safe to say that the sample is fool's gold (iron pyrite) rather than genuine gold. But don't worry, even though it may not be valuable, it still has its own unique charm... and a good sense of humor, just like yours truly, the Clown Bot!
To determine whether the sample is fool's gold or real gold, we can use the concept of density.
The formula for density is:
Density = mass / volume
We know the mass of the sample is 23.5 g. To find the volume of the sample, we can calculate the difference in water levels before and after the sample is added to the graduated cylinder.
Volume = Final volume - Initial volume
Volume = 52.2 mL - 47.5 mL
Volume = 4.7 mL
Next, we need to convert the volume from milliliters (mL) to cubic centimeters (cm3) because density is typically measured in g/cm3.
1 mL = 1 cm3
So, the volume of the sample is also 4.7 cm3.
Now, we can calculate the density of the sample:
Density = mass / volume
Density = 23.5 g / 4.7 cm3
Density ≈ 5.00 g/cm3
Comparing this density to the given densities, we see that the calculated density of 5.00 g/cm3 matches the density of fool's gold (d = 5.00 g/cm3).
Therefore, based on the calculated density, the sample is fool's gold (iron pyrite) rather than real gold.
To determine whether the sample is fool's gold or real gold, we can use the concept of density. Density is defined as the mass per unit volume of a substance. We know the mass of the sample, which is 23.5 grams, and we can calculate the change in volume by observing the change in water level in the graduated cylinder.
The change in volume is calculated by subtracting the initial water level from the final water level: 52.2 mL - 47.5 mL = 4.7 mL.
Now that we have the mass and volume, we can calculate the density using the formula:
Density = Mass / Volume
For fool's gold, which has a density of 5.00 g/cm³, we can calculate the expected density by converting the units of the values we have:
23.5 g / (4.7 mL * 0.001 L/mL) = 5000 g/L
Now, let's compare this value to the density of real gold, which is 19.3 g/cm³. We can similarly calculate the expected density for real gold:
23.5 g / (4.7 mL * 0.001 L/mL) = 5000 g/L
Comparing the calculated densities, we see that the calculated density of the sample (5000 g/L) is much closer to the density of fool's gold (5.00 g/cm³) than the density of real gold (19.3 g/cm³).
Therefore, based on the densities, it is more likely that the sample is fool's gold (iron pyrite) rather than real gold.