Chemistry 102 – Chapter 1 Summary and Review Answers 1. What are the measurements in meters and what is the order of smallest to largest? 100 nm, 0.010 μm and 100 pm Answer: First, convert the measurements to a common unit – the easiest would be meters. 100 nm = 100 × 10–9 m = (102 × 10–9) m = 10–7 m 0.010 μm = 0.010 × 10–6 m = (10–2 × 10–6) m = 10–8 m 100 pm = 100 × 10–12 m = (102 × 10–12) m = 10–10 m Now ordering is easy – based on the size of the exponent: 10–7 m > 10–8 m > 10–10 m or 100 nm > 0.010 μm > 100 pm 2. The density of gold is 19.3 g∙cm‐3. What is the length of an edge of 10.0 lb cube of gold in inches? Answer: You have a number of possible ways to solve this. One way involves converting the mass to grams and then determining the volume in cubic inches. This can be done in one step. 3
3
⎞
⎛ 454 g ⎞ ⎛ cm ⎞⎛ 1 in
= 14.4 in 3
(10.0 lb ) ⎜
⎟⎜
⎟⎜
3
3 ⎟
⎝ 1 lb ⎠ ⎝ 19.3 g ⎠⎝ 2.54 cm ⎠
[Try this calculation to make sure you get the correct answer – if you get 92.6 in3, you forgot to cube the volume of 2.543 cm3 (which is 16.4 cm3) and if you get 794 000 in3, you cubed the entire expression and not just 2.54.] Now to get the length of one edge, this is equal to the cube‐root as the volume of a cube is equal to the length of the side (all are equal) cubed. 3
14.4 in 3 = 2.43 in 3. It has been stated that to get perspective of sizes unfamiliar to us like “nano”, that one gallon of paint can cover Central Park in New York City to a thickness of 1.0 nm. According to this, what would then be the area of Central park in square miles? Answer: Again, there is more than one way to go about solving this exercise. One way, deal with the volume of the paint: determine the volume of the paint in nm3 (note: this will be a very large number and an otherwise useless way to represent a volume of paint ☺). You want to do this because you would like the area and you know the height (or thickness) is 1 nm. ⎛
⎞
⎛ 4 qt ⎞ ⎛ 0.9463 L ⎞ ⎛ 1 m3 ⎞ ⎜
1 nm3
⎟ = 3.8 × 1024 nm3
(1.0 gallon ) ⎜
⎟⎜
⎟⎜
⎟⎜
3
−
9
3
⎝ 1 gallon ⎠ ⎝ 1 qt ⎠⎝ 1000 L ⎠ (1× 10 ) m ⎟
⎝
⎠
Now, the thickness is 1 nm. So the volume divided by the thickness = the area or 24
2
3.79×10 nm . Now you want this area in square miles instead of square nanometers. This is a series of conversions using length conversions – so every conversion must be squared. If you do not get the correct answer, see the note in the exercise above. ⎛ (1× 10−9 )2 m 2 ⎞
2
2
⎞ ⎛ 1 ft 2
⎛
⎞⎛
( 3.8 ×10 nm ) ⎜⎜ nm2 ⎟⎟ ⎜ 1×10cm−4 m2 ⎟ ⎜⎜ 1 in2 2 ⎟⎟ ⎜ 144
in 2
⎝
⎠ ⎝ ( 2.54 ) cm ⎠ ⎝
⎝
⎠
24
2
⎞ ⎛ 1 mile 2
⎟ ⎜⎜
2
2
⎠ ⎝ ( 5280 ) ft
⎞
⎟ = 1.5 mile 2 ⎟
⎠
(If Central Park is 843 acres (which it is), what is the actual area of Central Part? 43 560 ft2 = 1 acre. The answer is 1.3 mile2 – pretty close approximation and very careful painting!)