## Using Your TI-85, TI-86 or TI-89 Equation-Solving Calculator

If you have a TI-85 or TI-86, you might want to check out the complete chapter
on equation solving for the TI-86. There is a similar chapter for the TI-89.

```[ENTER]       means "the ENTER key"
IDEAL        (uppercase letters) press [ALPHA] prior to each letter,
then the key for that letter. With the TI-89, these will be lowercase.
e q n        (lowercase letters) press [ALPHA] on the TI-89 or [2nd][alpha] on the
TI-85 or TI-86 prior to each letter, then the key for that letter
```

Note, the TI-89 makes no distinction between upper and lower case.

This Tutorial

This tutorial has several sections. We recommend you go through it in order.
Make sure you read the section corresponding to your calculator.
See also examples involving equilibrium and Boltzmann distribution problems.
Another web page you might be interested in is the JavaScript Graphing Calculator,
which has many pre-defined equations. You can use it directly, or
you can enter those equations into your TI calculator.

 Entering Equations TI-85,TI-86 TI-89 Loading Equations TI-85,TI-86 TI-89 Solving Equations TI-85,TI-86 TI-89 Math in the Solver TI-85,TI-86 TI-89 Editing and Saving Equations TI-85,TI-86 TI-89 Deleting Equations TI-85,TI-86 TI-89 Using Variables Outside the Solver TI-85,TI-86 TI-89 Constants TI-85,TI-86 TI-89 Conversion Factors TI-85,TI-86 TI-89 Special Notes TI-89

TI-85, TI-86top Entering Equations To get started, enter the following with upper/lower case exactly as shown below. This is a bit of a pain, as you have to be careful to use the [ALPHA] key (for uppercase) and [2nd][alpha] keys (for lowercase). But the payoff will be worth the trouble, because once these equations are in your calculator, you will not have to enter them again for the life of the calculator. Note that we use 'mol' instead of 'n' in the ideal gas law because 'n' is not allowed as a variable on some calculators. We use two versions of the ideal gas constant, 'Rg' and 'R', so that we can have one ideal gas constant (Rg) in units of L-atm/mol-K and one (R) in terms of Joules/mol-K. In addition, we use "d" instead of just because "d" is easier to enter from the keyboard. ```IDEAL = P * V = mol * Rg * T [ENTER] BOLT = nj/ni=e^(-dEij/(kb*T)) [ENTER] FREE = dG = dHo - T(dSo - R [LN] Q) [ENTER] ``` In each case, after pressing [ENTER] the calculator should respond with "done."
TI-89top Entering Equations To get started with the TI-89, first enter the solver. Press ```[APPS] to enter the solver ``` You should see a screen that looks like this: ```Enter Equation Eqn: ``` Enter the following equation. This is a bit of a pain, as you have to be careful to use the [ALPHA] key prior to each letter. But the payoff will be worth the trouble, because once these equations are in your calculator, you will not have to enter them again for the life of the calculator. Note that we use 'mol' instead of 'n' in the ideal gas law because 'n' might be used for all sorts of other meanings in other equations. We use two versions of the ideal gas constant, 'Rg' and 'R', so that we can have one ideal gas constant (Rg) in units of L-atm/mol-K and one (R) in terms of Joules/mol-K. ```Enter Equation Eqn: P * V = mol * Rg * T [ENTER] ``` Now to save this equation as IDEAL, press [F1] 2 [downarrow] ideal [ENTER] Two other equations you might want to save include: bolt ```nj/ni=e^(-dEij/(kb*T)) [ENTER] ``` free ```dG = dHo - T*(dSo - R * ln (Q)) [ENTER] ``` We use "d" instead of just because "d" is easier to enter from the keyboard. Also, "ln" is from pressing [2nd][LN]. Note that on the TI-89 you must show all multiplications explicitly with "*" and all functions must have parentheses. You can't just write "ln Q" as you can with the TI-85 or TI-86.
TI-85, TI-86top Loading Equations Press ```[2nd][SOLVER] to enter the solver [CLEAR] to clear out the current entry [2nd][RCL][IDEAL] to load the equation ``` The "IDEAL" key will appear as one of the "soft" function keys up near the screen, probably [F1]. Press [MORE] if you don't see it. Don't forget [2nd][RCL]! (If you forget these strokes, you can solve the equation, but you can't see what you're solving!)
TI-89top Loading Equations Press ```[APPS] to enter the solver [F1][downarrow] use the [>] key and scroll down to select the equation you want (choose "ideal" this time) [ENTER][ENTER][ENTER] to load the equation ``` You should now see a screen that looks like this: ```P * V = mol * Rg * T P= V= mol= Rg= T= bound={-1E14,1E14} ``` On the TI-89 calculator you have to be especially careful with the bounds. The default upper bound is not large enough for many of our problems. Be alert to this, and if you expect a number larger than 1 x 1014, be sure to adjust the upper bound EACH TIME you load a new equation. A value of 1E99 should be fine.
TI-85, TI-86, and TI-89top Solving Equations After loading the equation into the solver, you should see something like the following. (The heading "eqn:" does not show on the TI-89.) ```eqn:P*V=mol*Rg*T P= V= mol= Rg= T= bound={-1E99,1E99} ``` (If the upper bound is different from this, change it now.) Some of these variables may have numbers after them, depending upon what already may be defined in your calculator. The values will persist even after the calculator is turned off. If the first line reads "exp:IDEAL" and the second line reads "exp=" you have a TI-85 or TI-86 and forgot the [2nd][RCL] strokes. Clear out the equation and load it again. Let's solve the following problem: What is the volume of 1.00 mol of an ideal gas at 273 Kelvin if its partial pressure is 1.00 atm? Enter the values of all of the variables you know. Then go to the line for the variable you DON'T know and press [Clear] to erase whatever is there already and then [SOLVE] (F5 on the TI-85 or TI-86; F2 on the TI-89) to solve. We'll solve for volume (V) here: ```eqn:P*V=mol*Rg*T eqn:P*V=mol*Rg*T P=1 P=1 V= Press [SOLVE]==> V=22.40178759 mol=1 mol=1 Rg=.08205783 Rg=.08205783 T=273 T=273 bound={-1E99,1E99} bound={-1E99,1E99} ``` The answer is 22.4 L. (You have to think about precision and do the rounding off yourself. On homework and exams you probably won't get full credit if you answer "22.40178759." That's simply not correct, because it's too precise!)
TI-85, TI-86, and TI-89top Math in the Solver You can do math as you define your variables. For example, say you were given that the temperature was 15 oC. You could add 273 "on the fly": What is the volume of 1.00 mol of an ideal gas at 15 oC if its partial pressure is 1.00 atm? ```eqn:P*V=mol*Rg*T eqn:P*V=mol*Rg*T P=1 P=1 V= Press [SOLVE]==> V=23.63265504 mol=1 mol=1 Rg=.08205783 Rg=.08205783 T=15+273.15 T=288 bound={-1E99,1E99} bound={-1E99,1E99} ``` The volume of 1.0 mol of an ideal gas with a partial pressure of 1.0 atm at 15 oC is 23.6 L. Or maybe you want to solve for pressure, and the value you need is torr. For example, What is the partial pressure (in torr) of 1.00 mol of an ideal gas at 25oC if its volume is 2.00 L? ```eqn:P*V=mol*Rg*T eqn:P*V=mol*Rg*T P= Press [SOLVE]==> P=12.22661667 V=2 V=2 mol=1 mol=1 Rg=.08205783 Rg=.08205783 T=25+273 T=298 bound={-1E99,1E99} bound={-1E99,1E99} ``` This pressure is in atmospheres, so we need to multiply by the conversion factor "(760 torr)/(1 atm)" right there on that P line: ```eqn:P*V=mol*Rg*T eqn:P*V=mol*Rg*T P=12.22661667*760 Press [ENTER]==> P=9292.2286692 V=2 V=2 mol=1 mol=1 Rg=.08205783 Rg=.08205783 T=25+273 T=298 bound={-1E99,1E99} bound={-1E99,1E99} ``` The partial pressure of 1.00 mol of an ideal gas in a volume of 2.00 L at 25 oC is 9290 torr. (Note that we use three significant digits, because the temperature in Kelvin is 298. By adding 273 to 25, we increase the precision of the value.)
TI-85, TI-86top Editing and Saving Equations If you find you need to edit an equation, here's how you can do it quickly. First set it up exactly the way you want by editing the first line of the solver. Test it out to make sure it does just what you want it to do. This equation is now stored in the variable 'eqn'. Exit the solver. We're just going to define 'IDEAL' to be the value of the variable 'eqn', from the top line of the solver. You will need the [2nd][alpha] key sequence to get the lower-case e, q, and n: IDEAL = [2nd][RCL] e q n [ENTER][ENTER] You should see the following on your screen: ```Entered Calculator Reply --------------------- --------------------- IDEAL=P*V=mol*Rg*T Done ``` This same technique can be used for setting up equations in the first place. Just use the solver to get the equation the way you want it. Test it out and make sure it does what you want it to. Then exit the solver and key in the name you want to use for the equation--for example, 'IDEAL'. Then continue as above with = [2nd][RCL] e q n [ENTER][ENTER] Don't forget to use [2nd][alpha] for those lower case "e q n" letters. Editing and Saving Equations Just use the solver to get the equation the way you want it. Test it out and make sure it does what you want it to. Then, for the TI-89, while in the solver, save the equation by pressing [F1] 2 [downarrow] and entering the name you want to give the equation.
TI-85, TI-86top Deleting Equations On the TI-85 or TI-86, the easiest way to delete an equation is to turn it into a simple variable by storing the value 0 in it. Here we do it for the unwanted equation 'JUNK': ```Entered Calculator Reply --------------------- --------------------- 0 [STO>] JUNK [ENTER] 0 ``` 'JUNK' will be no longer be an equation and will be gone from the solver equation menu.
TI-89top Deleting Equations For the TI-89, press [2nd] [VAR-LINK]. Scroll down to the equation you want to delete and press [F1] 1.
TI-85, TI-86, and TI-89top Using Variables Outside the Solver The variables you define using the solver are still there after you exit the solver. Just use them like any other variable: 'x' is x, 'P' is P, 'dG' is dG, etc. For example, now I could key in (assuming I now have P = 9292.2286692 from my solver): [LN] [ALPHA] P [ENTER] ```Entered Calculator Reply --------------------- --------------------- ln P 9.13693370284 ```
TI-85, TI-86

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Constants

Several constants come with your calculator as "built-in" values and can be used in any calculation or equation. Here are some of the more useful ones for chemistry:
 Constant Name Value Units Avogadro Constant Na 6.0221367E+23 1/mol Boltzmann Constant k 1.380658E-23 J/K Ideal Gas Constant Rc 8.31451 J/mol/K Plank's Constant h 6.6260755E-34 J s Speed of Light c 299792458 m/s Mass of the Electron Me 9.1093897E-31 kg Charge on the Electron ec 1.60217733E-19 Coulombs
Note that one of these, k, is somewhat of a problem, because in chemistry "k" doesn't always refer to Boltzmann's constant. In this tutorial we've suggested you use "kb" instead of "k" for Boltzmann's constant.

TI-89

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Constants

Built-in constants are not worth their trouble on the TI-89. To access them, you enter an underscore [_] followed by the constant name. However (and this is a BIG however), they are returned with units. The capability of manipulating units is a feature of the TI-89 that is unique to it. While this might sound useful, there are two serious practical problems using this feature on the TI-89. First, once the units are there, you need to enter EVERY value you use with units. This is just incredibly time consuming. Second, the constants (with their units) cannot be used in the numeric solver. Since we will be making much use of the numeric solver, we suggest you igore the built-in constants on your TI-89. Here is a case were the TI-85 or TI-86 is much handier than the TI-89!

Instead, simply take the time now to enter the constants listed above into your calculator. To do this, simply enter the constant name followed by [=] and its definition. For example:

```6.0221367E23   [sto>] na [ENTER]
1.380658E-23   [sto>] kb [ENTER]
8.31451        [sto>] rc [ENTER]
6.6260755E-34  [sto>] h  [ENTER]
299792458      [sto>] c  [ENTER]
9.1093897E-31  [sto>] me [ENTER]
1.60217733E-19 [sto>] ec [ENTER]
```
TI-85, TI-86

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Conversion Factors

By pressing [2nd][CONV] you will find quite a few useful conversion factors, including those shown below. Press [MORE] to see additional categories and more conversions in each case.
 TEMP oC, oF, oK MASS gm, kg, lb PRESS atm, mmHg(torr), inHg PRESS atm, mmHg(torr), inHg ENERGY J, cal

The way you use these is very simple. Just enter a number, select the units the number is in, then select the units you want. Press [ENTER], and Presto! the conversion is done for you. For example:

```Entered               Calculator Reply
--------------------- ---------------------
9292 [mmHg] [atm] [ENTER]
12.2263157895
```

You can even do conversions right in the solver:

```eqn:P*V=mol*Rg*T                         eqn:P*V=mol*Rg*T P=12.22661667 [atm][mmHg][ENTER] ==> P=9292.2286692
V=2                                      V=2
mol=1                                    mol=1
Rg=.08205783                             Rg=.08205783
T=25+273                                 T=298
bound={-1E99,1E99}                       bound={-1E99,1E99}
```
TI-89

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Conversion Factors

The TI-89 does have conversion factors, but they are not useful in practice. The problem is that (a) they are annoyingly difficult to find and (b) once again, they require all numbers to be entered carefully with units.

TI-89top Special Notes Certain older TI-89 calculators (vintage 2000?) appear to have a problem with the equation solver. On these calculators, the following equation cannot be solved for dEij: ```nj/ni=e^(-dEij/(kb*T)) ``` It's not clear what the problem is, but the quick way around it is to enter the equation in a slightly different form: ```ln(nj/ni)=-dEij/(kb*T) ``` Solving this equation, which is really the same as the first, is no problem on newer calculators because their operating system uses a different (better) algorithm for its numeric solver. If you find this to be a problem, consider updating your calculator. You will need a cable to connect your calculator with a newer TI-89 calculor. Then, on your calculator, press [VAR-LINK]"receive" and on the other (newer!) calculator, press [VAR-LINK]"send OS."
revised 10:56 AM 2/17/2003 BH