옴스테드 화학 1장 연습문제 (4판)

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옴스테드 화학 1장 연습문제 (4판)에 대한 보고서 자료입니다.

목차

Atoms, Molecules, and Compounds

The Periodic Table of the Elements

Characteristics of Matter

Measurements in Chemistry

Calculations in Chemistry

Chemical Problem Solving

Additional Paired Problems

More Challenging Problems

Group Study Problems

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sition of pennies during this time period? (b) In 1979,
pennies were 95% copper and 5% zinc by mass. Calculate the volume of a penny (see Table 1-4). (c) Measure the diameter of a penny, then determine its thickness to as many significant figures as you can. (d) Determine the mass percentages of copper and zinc in post-1981 pennies. (e) Post-1981 pennies are essentially pure zinc with a thin copper overlayer. Determine the thickness of the copper overlayer (this will be easier if you neglect the overlayer around the circumference).
We are told that the volume of the penny has not changed, so the fact that the mass of the penny changed in 1982 tells us that the density of the penny changed in that year. From Table 14, we see that zinc (7.14 g/cm3) is less dense than copper (8.96 g/cm3).
(a) The density change must be due to a change in composition of the penny. Because the mass decreased, the density also decreased, so post981 pennies contain more zinc relative to copper than pennies from 1981 and before.
(b) Before we can calculate the volume of a penny, we need to know the density of the penny, which we find by taking the weighted average of densities of the pure metals:
penny density = (0.95)(8.96 g/cm3) + (0.05)(7.14 g/cm3) = 8.87 g/cm3
We also need to know the average mass of pre982 pennies, which we find by adding the three masses and dividing by 3:
m (average) = (3.075 + 3.095 + 3.066)/3 = 3.08 g (precise to two decimals)
Now we rearrange the density equation, solving for volume:
(c) The diameter of a penny is 1.9 cm, giving a radius of 0.95 cm. Rearrange the equation for the volume of a cylinder to solve for h, the height (thickness):
(This result has only two significant figures, because the diameter of a penny cannot easily be measured to better than 1 mm.)
(d) Post981 pennies have the same volume as earlier pennies. We can calculate their density using the average mass of these pennies:
This density must be the weighted average of the densities of the two components of pennies, zinc and copper. If we let x be the fraction that is zinc, then (1x) is the fraction that is copper:
7.29 g/cm3 = x (7.14 g/cm3) + (1 x)(8.96 g/cm3)
Multiply out, group terms in x, and solve for x:
7.29 = 7.14 x + 8.96 8.96 x from which 1.67 = 1.82 x and x = 0.918
Post981 pennies are 91.8% Zn and 8.2% Cu.
(e) First, calculate the masses of zinc and copper in a post981 penny. Then calculate the volume of each metal. Assume all the volume of zinc is in the interior and the volume of copper is in two layers, one on top and one on the bottom.
m(Zn) = (0.918)(2.53 g) = 2.32 g and m(Cu) = (0.082)(2.53 g) = 0.2075 g
Use the density of pure copper to calculate the volume of the copper layers:
We already know the diameter of a penny, so we can calculate the thickness of the copper layer in the same fashion as we calculated the thickness of a penny in part (c):
There are two layers, so divide by 2 and round to two significant figures to get the thickness of each layer:

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