Consider a piece of gold jewelry that weighs 9.35 g and has a volume of 0.690 cm3 . The jewelry contains only gold and silver, which have densities of 19.3 g/cm3 and 10.5 g/cm3, respectively. If the total volume of the jewelry is the sum of the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry.
Oh, I see we're doing some jewelry math! Let's find out how much gold we have in this shiny piece.
First, we need to find the mass of the gold in the jewelry. Since the density of gold is 19.3 g/cm3, we can use the formula: mass = density × volume.
The volume of the gold is given as 0.690 cm3, so the mass of the gold is: mass_gold = density_gold × volume_gold = 19.3 g/cm3 × 0.690 cm3.
Now let's figure out how much silver we have. Since the total volume of the jewelry is the sum of the gold and silver volumes, we can subtract the gold volume from the total volume to find the silver volume: volume_silver = total_volume - volume_gold.
The total volume is given as 0.690 cm3, so the silver volume is: volume_silver = 0.690 cm3 - 0.690 cm3 = 0 cm3.
Oops! It seems we made a little mistake there. According to the given information, the silver volume is 0 cm3, which means there is no silver in the jewelry. It's all gold!
Therefore, the percentage of gold (by mass) in the jewelry is 100% because there is no silver. That's one golden piece of jewelry!
To calculate the percentage of gold (by mass) in the jewelry, we need to determine the mass of gold and the mass of silver in the jewelry.
Let's start by finding the volume of silver in the jewelry. Since we know the total volume of the jewelry and the volume of gold, we can subtract the volume of gold from the total volume to find the volume of silver:
Volume of silver = Total volume - Volume of gold
= 0.690 cm^3 - 0.690 cm^3 [since there is only gold and silver in the jewelry]
= 0 cm^3
From the calculation, we can see that the volume of silver in the jewelry is 0 cm^3. This indicates that the jewelry is made entirely of gold.
Now, let's calculate the mass of gold in the jewelry. We know the density of gold is 19.3 g/cm^3 and the volume of gold is 0.690 cm^3. We can use these values to find the mass of gold:
Mass of gold = Density of gold * Volume of gold
= 19.3 g/cm^3 * 0.690 cm^3
= 13.317 g
Since the jewelry weighs 9.35 g, and this weight is entirely due to the gold, we can conclude that the jewelry is 100% gold.
Therefore, the percentage of gold (by mass) in the jewelry is 100%.
To calculate the percentage of gold in the jewelry, we need to determine the mass of the gold in the jewelry. Here's how we can do that:
1. Calculate the volume of silver in the jewelry:
To do this, we subtract the volume of gold from the total volume of the jewelry.
Volume of Silver = Total Volume of Jewelry - Volume of Gold = 0.690 cm^3 - Volume of Gold
2. Convert the volume of silver to mass:
We can multiply the volume of silver by the density of silver to find its mass.
Mass of Silver = Volume of Silver * Density of Silver = (0.690 cm^3 - Volume of Gold) * 10.5 g/cm^3
3. Calculate the mass of gold in the jewelry:
The mass of gold in the jewelry is the total mass of the jewelry minus the mass of silver.
Mass of Gold = Total Mass of Jewelry - Mass of Silver = 9.35 g - (0.690 cm^3 - Volume of Gold) * 10.5 g/cm^3
4. Calculate the percentage of gold:
Lastly, we divide the mass of gold by the total mass of the jewelry and multiply by 100 to get the percentage.
Percentage of Gold = (Mass of Gold / Total Mass of Jewelry) * 100
Now we can plug in the given values and calculate the percentage of gold in the jewelry.
If there are g grams of gold, then add up the volumes (mass/density):
g/19.3 + (9.35-g)/10.5 = 0.690
g = 4.6
So, the % mass of gold is
4.62/9.35 = 0.49 = 49%