Chemistry help!

Question

A balloon is filled with air so that its volume is 5.6 L at 25.0 degrees celsius. Is is then lowered into a vat of liquid nitrogen so that is reaches a temperature of -196.0 degrees celsius. Assuming that the pressure stays constant, what is the new volume?

Answer 1

First, remember that for any gas law problem, you don't need to memorize all of the

different gas equations. Only one, the Ideal Gas Law, FV=nRT is needed. Any equation

you need can easily be derived from this by placing all unchanging values on one side

of the "=" and all changing values on the other side.

 

In this problem, what are the unchanging values? Write them all down:

 

P; the pressure does not change because we are told that it does not.

n; n is the number of moles of gas-it doesn't change; no gas escapes or is added.

R; R is the Universal gas constant-it always has values of

 

0.81206 (L • atm)/(mol • K)  OR 8.314 J/(mol • K)

 

 The value of R you use depends on the units given in the problem;

 

The values that are changed are:

 

T; Temperature (always put into Kelvins);

in this case T_initial = 25 ^oC + 273.15 = 298.15 K (the STP temp)

      and      T_final = -196 ^oC+273.15 = 77 .15 K

 

 K = ^oC + 273.15 COMMIT TO MEMORY!

 

V; Volume is the value changing to some new value:

     V_initial = 5.6 L                                                               
     V_final =  ? (the answer)

 

SO: rearrange the equation to put unchanging values on one side

and changing values on the other:

 

PV=nRT    divide both sides by T    

 

We will use terms T_initial and T_final  or T_{i and} T_f

                      and V_initial and V_final  or V_i and V_f

 

    P_iV_i = nR   now, divide both sides by V
     T_i                                                Write these math functions out, and see how things

                                                        cancel if you struggle with algebra

 

To get V_i/T_i = nR/P  and BECAUSE the value of nR/P doesn't change,   

 

Vi/T_i =   nR/P  = V_f/T_f                                                 

 

THIS IS CHARLE'S LAW: V_i =  V_f      we can do this because if

                                          T_i     T_f         A = B = C, then A = C

 

SO take Charle's Law equation, and rearrange for the unknown, V_f

 

V_f = V_iT_f = (5.6 L)(77.15 K) = 1.4 L  

         Ti          298.15 K

NOTE the K's cancel, and our answer is in Liters, as it should be.

Be meticulous and write down all your units, make sure they cancel

so your answer has the right units. If they don't cancel while doing the math,

SOMETHING IS WRONG, and start over.

Also, make sure to include the units in the answer. The question says

"what is the new volume?" so an answer of 1.4 is not completely accurate.

If the question asked "what is the new volume in liters?" then 1.4 is acceptable.

 

Check sig figs - the least precise measurement is 5.6 L, so the answer can

be no more precise than having 2 sig figs.

Finally, the last step of all problems is to ask yourself -

"does the answer make sense?"

 

In this case, a balloon of gas is cooled in liquid nitrogen

(you may recall a class demonstration); as you cool a gas, the molecules

have less energy and move slower, hitting the container walls with less

force, so the volume should go down. Going from 5.6 L to 1.4 L seems perfectly

reasonable if you cool the balloon. If the volume went from 5.6 L to 23,591.331 L,

alarm bells should be ringing!

 

Why did I go to the trouble to derive Charle's Law? If you are taking an exam

and freeze-just relax; you can derive any of the gas laws from PV=nRT.

AND if more than two of the parameters change, you MUST know how to use PV=nRT.   

 

SUMMARY: Changing values on one side, unchanging values on the other,

remove the unchanging values and set initial values equal to final values.

Put T into Kelvins. NOW, try the same thing for Boyle's Law.

Answer 2

Because this problem involves volume and pressure, we use Charles's Law:

 

V₁/T₁ = V₂/T₂

 

Remember to convert Celsius to Kelvin, which gets rid of any negative values for temperature. To do this, we simply add 273.15 to the Celsius temperature:

 

T₁ = 25.0 + 273.15 = 298.15K

T₂ = -196.0 + 273.15 = 77.15K

 

Now, rearrange the equation to solve for the final volume:

 

(T₂)(V₁/T₁) = V₂

 

Finally, plug in our values and solve:

 

(77.15)(5.6/298.15) = 1.4