# If #"3.50 mols"# of freon-12 gas was added to #"7.48 mols"# of it, and it started at #"28.7 L"#, what is its final volume?

##### 2 Answers

#### Answer:

When you pay peanuts you get monkeys..........

#### Explanation:

Generally, the answers are checked by experienced posters, and you will see many corrections and additions to answers. But this is not a cheat site; the emphasis is on the explanation not the final result, which the student is obligated to provide themselves. Learning will not occur otherwise.

Old Avogadro's Law states that

And thus

And so

And so

#V_1 = "19.6 L"#

That is, if freon-12, or

Well, if we assume the **Freon-12** gas is ideal, then we can use the ideal gas law:

#PV = nRT# ,where:

#P# is thepressurein, say,#"atm"# .#V# is thevolume, usually in#"L"# .#n# is themolsof ideal gas.#R = "0.082057 L"cdot"atm/mol"cdot"K"# is theuniversal gas constant, if pressure is in#"atm"# and volume is in#"L"# .#T# istemperaturein#"K"# .

There were unstated conditions, and they were:

- constant temperature
- constant pressure

Only then can we come up with **Avogadro's principle**... We set initial and final states as:

#PV_1 = n_1RT#

#PV_2 = n_2RT#

And if we rearrange, we realize that...

#V_1/n_1 = V_2/n_2 = (RT)/P#

i.e. that the *molar volume* of the freon gas remains constant (as it must, if it is to remain the same gas at the same temperature and pressure).

So, if we add

#n_2 = overbrace("7.48 mols")^(n_1) + overbrace("3.50 mols")^(Deltan)#

or that **initial volume** is:

#color(blue)(V_1) = n_1/n_2 xx V_2#

#= "7.48 mols"/"10.98 mols" xx "28.7 L"#

#=# #color(blue)("19.6 L")# to three sig figs.

And as always, we should check that our answer makes physical sense.

We added **more mols of gas** at constant temperature and pressure, so the balloon SHOULD **expand**, *directly proportional to* the increase in mols of gas... and it does!

#V_2/V_1 -= "28.7 L"/"19.6 L" stackrel(?" ")(=) ("10.98 mols")/("7.48 mols") -= n_2/n_1#

#1.464 ~~ 1.468# #color(blue)(sqrt"")#

But of course, this calculation is only valid for ideal gases. We are not given the temperature or pressure, so if we are in an evacuated refrigerator, we could very well be staring at one of the worst examples of an ideal gas...