Unit Conversions and Temperature Scales in General Chemistry

Unit Conversions

Understanding Unit Factors

In chemistry, it is often necessary to convert measurements from one unit to another. This is accomplished using unit factors, which are ratios that express the relationship between two units.

• Unit factor: A ratio equal to one, used to convert from one unit to another without changing the value of the measurement.

• Example: $16\ \text{oz}/1\ \text{lb}$ or $1\ \text{lb}/16\ \text{oz}$

• Example: $453.59\ \text{g}/1\ \text{lb}$ or $1\ \text{lb}/453.59\ \text{g}$

• Example: $1\ \text{in.}/2.54\ \text{cm}$ (alternative: $2.54\ \text{cm}/1\ \text{in.}$)

These factors do not change the actual measurement, only the unit in which it is expressed.

Steps for Converting Units

1. Use unit factors that relate the given unit to the desired unit.

2. Derive the orientation of the unit factor by looking at the given unit and the desired unit.

3. Perform the mathematical operation necessary (make sure appropriate units cancel).

4. Check the significant figures and the units.

5. Does the answer make sense?

Example Problems

• Distance Conversion: The left field wall at Wrigley Field in Chicago measures 355 ft. What is this distance expressed in meters?

• Gas Mileage Conversion: An automobile achieves a gas mileage of 36.1 mi/gal. How many kilometers can it travel on 1 L of gasoline?

Additional info: To solve these, use the appropriate unit factors (e.g., 1 ft = 0.3048 m, 1 mi = 1.609 km, 1 gal = 3.785 L).

Temperature Scales

Common Temperature Scales

There are three commonly used temperature scales in science and engineering:

• Kelvin (K): Used commonly in science. No degree symbol is used.

• Celsius (°C): Also called Centigrade. Used in most of the world and in scientific contexts.

• Fahrenheit (°F): More common in engineering and in the United States.

Writing Temperature Units

• Always leave a space between the number and its unit (e.g., 25 °C, 300 K).

• For Celsius and Fahrenheit, use the degree symbol (°C, °F). For Kelvin, simply use K (not °K).

Converting Between Temperature Scales

• Kelvin and Celsius:

$T_K = T_C + 273.15$

$T_C = T_K - 273.15$

• The difference of 273.15 is due to the different zero points of the scales.

• Fahrenheit and Celsius:

These scales are related using water as the standard:

• Boiling point of water: 212 °F (Fahrenheit), 100 °C (Celsius)

• Freezing point of water: 32 °F (Fahrenheit), 0 °C (Celsius)

This leads to the following relationships:

$T_C = \frac{5}{9} (T_F - 32)$

$T_F = \frac{9}{5} T_C + 32$

Example Problems

• Normal body temperature: 98.6 °F. What is this temperature in Kelvin?

• Outer space temperature: ~4 K. What is this temperature in degrees Fahrenheit?

Additional info: To solve, first convert between Fahrenheit and Celsius, then between Celsius and Kelvin as needed.

Summary Table: Temperature Scale Relationships

Scale	Freezing Point of Water	Boiling Point of Water	Degree Size
Celsius (°C)	0	100	1 °C
Fahrenheit (°F)	32	212	1 °F = 5/9 °C
Kelvin (K)	273.15	373.15	1 K = 1 °C

Additional info: The Kelvin scale is an absolute scale, starting at absolute zero (0 K), the theoretical lowest possible temperature.