Question

I don't understand how to use equation three to figure out the composition of a penny's zinc % and copper % using the data I collected. Can someone show me how to do it?

Trial 2 Data Table 4: The Penny Number of pennies Total mass of pennies (g) Initial volume of water (mL) Final volume of water (mL) Volume the pennies occupy (mL) Density of a penny (g mL) Average density of a penny (g mL-1) Trial 1 25 pennies 62세1g pennies 25 mL 35 mL. 28 ml 33 ml (3 mL .377 9ImL -- D. 80q- rnL | 17. The percent composition of t he penny can now be determined by noting that the average density determined in step 16 represents a weighted average o densities of the two component metals, copper and zinc. This weighted average can be expressed mathematically as follows x (copper density) + (1-x) (zinc density) = average density of the penny Equation 3 where x = the fraction of the penny that is comprised of copper 1-x = the fraction of the penny that is comprised of zinc Using the densities from Table 4 and Equation 3 determine the values of x and 1 - x and then convert the decimal values to percentages by multiplying each by 100. Report your final answer below Composition of the modern penny = % zinc and % copper

Answer 1

You haven’t included the density values given in your table 4. I shall use values obtained from internet sources.

The change in volume for trial 2 will be 10.0 mL; hence the density of the pennies is (69.907 g)/(10 mL) = 6.9907 g/mL. The average density is ½*(6.2411 + 6.9907) g/mL = 6.6159 g/mL.

x is the fraction of copper in the penny. Since the penny is comprised only of copper and zinc, hence the sum total of the fractions of copper and zinc must be 1.0. Therefore, the fraction of zinc in the penny is (1 – x).

Density of copper is 8.96 g/mL while the density of zinc is 7.13 g/mL.

Plug in the values in the equation to get

x*(8.96 g/mL) + (1 – x)*(7.13 g/mL) = 6.6159 g/mL

===> 8.96x + 7.13 – 7.13x = 6.6159

===> 1.83x = -0.5141

We run into a trouble here. The value should have been positive. Kindly check our data. I shall ignore the negative sign and work with the positive value to show you how its done.

1.83x = 0.5141

===> x = (0.5141)/1.83 = 0.2809 ≈ 0.281

Therefore, (1 – x) = (1 – 0.281) = 0.719.

Thus, percentage of copper in the penny = (0.281)*100% = 28.1% and the percentage of zinc in the penny is (0.719)*100% = 71.9% (ans).