'Copper' pennies actually contain very little copper. If a penny contains 91.768 % of its total volume zinc and 8.232 % of its total volume copper, what is its density? (d of Cu = 8.95 g/cm3; d of Zn = 7.14 g/cm3.)
Assume you had 100cm^3 of pennies.
Then you would have a mass of 91.768*densityzinc, and a mass of 8.232*density copper. Add those to get the total mass. You know the mass, so
find density (mass/volume)
To find the density of the penny, we need to calculate the average density based on the proportion of zinc and copper in its composition.
First, let's assume that we have a 100 cm³ penny.
Given that 91.768% of its volume is zinc and 8.232% is copper, we can calculate the volume of zinc and copper in the penny:
Volume of zinc = (91.768/100) * 100 cm³ = 91.768 cm³
Volume of copper = (8.232/100) * 100 cm³ = 8.232 cm³
Next, we need to calculate the mass of each metal in the penny, using the provided densities:
Mass of zinc = volume of zinc * density of zinc = 91.768 cm³ * 7.14 g/cm³
Mass of copper = volume of copper * density of copper = 8.232 cm³ * 8.95 g/cm³
Now we can find the total mass of the penny by summing the masses of zinc and copper:
Total mass = mass of zinc + mass of copper
Finally, we can find the density of the penny by dividing the total mass by the total volume:
Density = Total mass / Total volume
By plugging in the values and performing the calculations, you will arrive at the density of the penny.