The reference value for the density of pennies is 7.1890 g/cm³. The percent error for the method using copper is approximately 24.37%, and for zinc, it is approximately 0.68%.
To calculate the reference value for the density of the pennies, we can use the weighted average of the densities of copper (Cu) and zinc (Zn) based on their respective percentages in the penny.
a. The penny is composed of 2.5% Cu and 97.5% Zn. To find the overall density (rho_overall), we use the formula:
rho_overall = (percentage of Cu * density of Cu) + (percentage of Zn * density of Zn)
rho_overall = (0.025 * 8.94) + (0.975 * 7.14)
rho_overall = 0.2235 + 6.9655 = 7.1890 g/cm³
The reference value for the density of the pennies is 7.1890 g/cm³.
b. The densities of Cu and Zn provided are 8.94 g/cm³ and 7.14 g/cm³, respectively. To compare the methods, we calculate the percent error for each:
Percent Error = (|Experimental Value - Theoretical Value| / |Theoretical Value|) * 100
Percent Error for Cu = (|8.94 - 7.1890| / |7.1890|) * 100 ≈ 24.37%
Percent Error for Zn = (|7.14 - 7.1890| / |7.1890|) * 100 ≈ 0.68%
The question probable may be:
Calculate the reference value for the density of the pennies using the following information.
a. U.S. pennies are 2.5% Cu and 97.5% Zn
b. Metal Density(g/cm3)
Zinc 7.14
Copper 8.94
Calculate the percent error for both methods used.