A 9.35 gram of ring with it's volume of 0.654 cm3 is an alloy of gold and with density of gold and silver respectively 19.3 g/cm3 and 10.5 g/cm3 assume there is no change in volume when pure metals are mixed. calculate volume of gold?
mass = volume x density or
vol = mass/density
vol Au + vol Ag = total vol
Let x = mass Au then
9.35-x = mass Ag
(x/19.3) + (9.35-x)/10.5 = 0.654
Solve for x = mass Au, then
x/19.3 = vol Au.
To calculate the volume of gold in the alloy, we need to use the concept of mass percent and the difference in densities between gold and silver.
First, let's calculate the mass of the alloy. You already mentioned that the mass of the ring is 9.35 grams.
Next, we need to find the total volume of the alloy. The volume of the ring is given as 0.654 cm^3.
Now, we can find the density of the alloy using the formula:
Density = Mass / Volume
Given that the density of the alloy is the average of the densities of gold and silver, we can use this formula to find the density of the alloy:
Density of alloy = (Density of gold + Density of silver) / 2
Now that we have the mass and volume of the alloy, we can substitute these values into the density formula to find the density of the alloy:
Density of alloy = Mass of alloy / Volume of alloy
Rearranging the equation, we can solve for the volume of the alloy:
Volume of alloy = Mass of alloy / Density of alloy
Now we can calculate the volume of the gold in the alloy.
The mass percent of gold in the alloy is given by the formula:
Mass percent = (Mass of gold / Total mass of alloy) * 100
To find the mass of gold, we can use this equation:
Mass of gold = Mass percent * Total mass of alloy / 100
Finally, we can calculate the volume of gold using the density of gold:
Volume of gold = Mass of gold / Density of gold
Substituting the given values and calculating these equations, we can find the volume of gold in the alloy.