In the Classroom
Calculating Units with the HP 48G Calculator Matthew E. Morgan Department of Chemistry, 2355 Fairchild Dr., Suite 2N341, U.S. Air Force Academy, CO 80840-6230;
[email protected].
Manipulating units of measure is one of the most important yet difficult-to-master concepts introductory chemistry students face. The Hewlett Packard HP 48G graphing calculator is able to manipulate units as well as perform numerical and symbolic calculations (1). The HP 48G’s units function can make simple calculations, such as converting grams to moles, or more complex unit analysis, such as gas law calculations. Units are attached to numbers using the UNITS menu located above the HP 48’s “6” key. To input a 35.0-gram value, type 35.0 on the keypad; then press the key and 6 . Selectable units for many measurable quantities will be displayed above the menu keys. After F and then B are pressed, the 35.0 in the calculator display changes to 35.0_g. This data object has both a numerical and a unit component. If this 35.0-gram sample was magnesium and the number of moles in the sample was to be calculated, the sample would need to be divided by magnesium’s molar mass, 24.31 g/mol. Magnesium’s molar mass value is input according to Table 1. Operations such as inverse ( 1/x ) can be applied to these number–unit objects. Both the number and the units will be inverted. For example, 24.31g/mol becomes 0.04114 mol/g.
When the 35.0_g object is divided by 24.31_g/mol, the result is 1.44_mol. If a student inadvertently multiplies the two values together rather than divides, the result would be 8.51 × 102 g2/mol. The units on this answer are obviously wrong. The units evaluation ability of the HP 48 can be applied to the classic problem of finding the volume of one mole of an ideal gas at standard temperature and pressure (STP). Table 2 shows HP 48 keystrokes and their result on the HP 48 display. 6 NOTE: The key combination brings up the UNITS menu on the calculator. The NXT key changes to the next page of menu choices, and the through keys select from the UNITS menu. Also, while the SI abbreviation for liters is L, the HP48 displays this unit as l. Even complicated exercises such those using the van der Waals gas equation can be accomplished using numbers and units on the HP 48G. It is left to the instructor and student to decide whether displaying units on a calculator is worth the extra keystrokes. A
F
Literature Cited 1. Information was obtained from the Hewlett Packard HP 48G Users Guide; Hewlett Packard: Corvalis, OR, 1993.
Table 1. Displaying Units for Molar Mass of Magnesium HP 48 keys pressed
Calculator Display Comment
24.31
24.31
The numerical value
24.31_g
Attach unit (grams) to number
1
Number of moles
1_mol
Attach unit (moles) to number
24.31_g/mol
Molar mass of magnesium
6
F
B
1 6
F
NXT
NXT
B
÷
Table 2. Calculating Gas Volume Using Units Keystroke 1
HP 48 Display 6
.08206
F
NXT
6
1
6
NXT
1
6
NXT
1
6
273.15
C
NXT
D E F
6
NXT
NXT
B
X
C
÷
NXT
NXT
1_mol
A
0.08206_l 0.08206_l * atm 0.08206_l * atm/K
B
E
C
÷
0.08206_l * atm/(K*mol) 273.15_K 22.414_l*atm/mol
X
22.414_l*atm
X
1
B
6
NXT
D
B
÷
22.414_l
JChemEd.chem.wisc.edu • Vol. 76 No. 5 May 1999 • Journal of Chemical Education
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