Question 2.16: Density as a Conversion Factor The gasoline in an automobile......
Density as a Conversion Factor
The gasoline in an automobile gas tank has a mass of 60.0 kg and a density of 0.752 g/cm^3. What is its volume in cm^3?
| SORT
You are given the mass in kilograms and asked to find the volume in cubic centimeters. Density is the conversion factor between mass and volume. |
GIVEN: 60.0 kg
density = 0.752 g/cm^3 FIND: volume in cm^3 |
| STRATEGIZE
Build the solution map starting with kg and ending with cm^3. Use the density (inverted) to convert from g to cm^3. |
SOLUTION MAP
kg \underset{\frac{1000 g}{1 kg} }{\longrightarrow } g \underset{\frac{1 cm^3}{0.752 g} }{\longrightarrow } cm^3
RELATIONSHIPS USED 0.752 g/cm^3 (given in problem) 1000 g = 1 kg (from Table 2.2) |
| SOLVE
Follow the solution map to solve the problem. Round the answer to three significant figures to reflect the three significant figures in the given quantities. |
SOLUTION
60.0 \cancel{ kg}\times \frac{1000 \cancel{ g}}{1 \cancel{ kg}}\times \frac{1 cm^3}{0.752 \cancel{ g}} = 7.98 \times 10^4 cm^3 |
| CHECK
Check your answer. Are the units correct? Does the answer make physical sense? |
The units of the answer are those of volume, so they are correct. The magnitude seems reasonable because the density is somewhat less than 1 g/cm^3; therefore, the volume of 60.0 kg should be somewhat more than 60.0 × 10^3 cm^3. |
Table 2.2
| SI Prefix Multipliers | ||||
| Prefix | Symbol | Meaning | Multiplier | |
| tera- | T | trillion | 1,000,000,000,000 | (10^{12}) |
| giga- | G | billion | 1,000,000,000 | (10^{9}) |
| mega- | M | million | 1,000,000 | (10^{6}) |
| kilo- | k | thousand | 1,000 | (10^{3}) |
| hecto- | h | hundred | 100 | 10^{2} |
| deca- | da | ten | 10 | 10^{1} |
| deci- | d | tenth | 0.1 | (10^{-1}) |
| centi- | c | hundredth | 0.01 | (10^{-2}) |
| milli- | m | thousandth | 0.001 | (10^{-3}) |
| micro- | µ | millionth | 0.000001 | (10^{-6}) |
| nano- | n | billionth | 0.000000001 | (10^{-9}) |
| pico- | p | trillionth | 0.000000000001 | (10^{-12}) |
| femto- | f | quadrillionth | 0.000000000000001 | (10^{-15}) |