the current U.S. penny is only 2.5% copper the remaining portion is zinc. Given the density of copper as 8.94 g/cm and the density of zinc is 6.57 g/cm, calculate the density of a penny.
Frankly I don't think this problem is workable unless we make some assumptions which probably are not true. The penny has a mass of 2.50g
mass Cu = 2.50*0.025 = about 0.06 g
mass Zn = 2.50*0.975 = about 2.44 g
volume Cu = m/d = 0.06/8.94 = about 0.007 cc
volume Zn = m/d = 2.44/6.57 = about 0.371 cc
Total volume if we assume volumes are additive (they aren't) = 0.378
Then density penny = m/v = 2.50/0.378 = about 6.61 g/cc.
Volumes are not additive, especially in solid alloys but with such a low concn of Cu and a high concn of Zn, this number of 6.61 g/cc (almost the same as pure Zn) must be reasonably close. You could measure the density rather easily. Place exactly 15 mL water in a 25 mL graduated cylinder, add 10 weighed pennies and read the volume of water. The volume is the difference in the volume levels with and without pennies. Then I would divide the mass by 10 to find the mass of one penny, divide volume by 10 to find volume of one penny, then divide m/v to find density of one penny.
To calculate the density of a penny, we need to know the composition of the penny by mass. In this case, we are given that the current U.S. penny is 2.5% copper and the remaining portion is zinc.
Let's assume the mass of the penny is 1 unit for simplicity. Therefore, the mass of the copper in the penny would be 0.025 units (2.5% of 1 unit), and the mass of the zinc would be 0.975 units (the remaining 97.5%).
Now, we can calculate the volume of each metal using their respective densities. The volume of copper would be:
Volume of copper = Mass of copper / Density of copper = 0.025 units / 8.94 g/cm³
Similarly, the volume of zinc would be:
Volume of zinc = Mass of zinc / Density of zinc = 0.975 units / 6.57 g/cm³
Since the total volume of the penny is the sum of the volumes of copper and zinc, we can calculate the total volume as:
Total volume = Volume of copper + Volume of zinc
Finally, we can calculate the density of the penny using the formula:
Density = Mass / Volume
So, the density of the penny would be:
Density = 1 unit / Total volume
To get the density in g/cm³, we can convert the units appropriately when performing the calculations.
To calculate the density of a penny, you need to know the mass and volume of the penny. Since the composition of the penny is given, you can calculate the density using the densities of copper and zinc.
First, let's define the composition of the penny: 2.5% copper and the remaining portion (97.5%) zinc.
To proceed with the calculation, there are a few assumptions we need to make:
1. We will assume that the densities of copper and zinc remain constant throughout the penny.
2. We will assume that the penny is solid and has a uniform composition.
Now, let's calculate the density of the penny:
Step 1: Calculate the density of copper in the penny:
- copper_density = 2.5% * copper_density = 0.025 * 8.94 g/cm³
Step 2: Calculate the density of zinc in the penny:
- zinc_density = 97.5% * zinc_density = 0.975 * 6.57 g/cm³
Step 3: Calculate the overall density of the penny:
- penny_density = copper_density + zinc_density
The overall density of the penny can be calculated by adding up the densities of the individual components (copper and zinc) based on their respective percentages.
Now, substitute the values and calculate the density:
copper_density = 0.025 * 8.94 g/cm³ = 0.2235 g/cm³
zinc_density = 0.975 * 6.57 g/cm³ = 6.39975 g/cm³
penny_density = copper_density + zinc_density = 0.2235 g/cm³ + 6.39975 g/cm³
Therefore, the density of a penny is approximately 6.62325 g/cm³.