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Gas Law Examples and Practice Problems

SECTION 5 - Gases


In this video blog post, we'll do several gas law practice problems.  The first two examples only contain "1 situation."

These are Ideal Gas Law conditions -- only 1 situation.

Ideal Gas Law Examples

ex A sample of H2 gas occupies a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm.  How many moles of hydrogen are present?
_________
answer:

➞  PV = nRT   ➞  n = PV / RT

➞  n  =  (1.5 atm) (8.56 L)  /  (0.0821 L.atm/K.mol) (273 K)

➞  n  =  0.57 mol H2

Here's the same solution, but with a natural flow...

Ideal Gas Law Example

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ex:  Calculate the volume of 0.845 mol of nitrogen gas at a pressure of 699.2 torr and a temperature of 315 K.
_________
answer:

➞  we have to convert pressure from torr to atm

➞  given:

       n = 0.845 mol N2
       T = 315 K
       V = ?
       P = 699.2 torr

    (699.2 torr / 1) . (1 atm / 760 torr)  =  0.9200 atm

➞  PV = nRT      ➞  V = nRT / P

➞  V = nRT / P   =   (0.845)(0.0821)(315) / 0.9200  =  23.8 L N2

And, here's an easier-to-follow view of the above process:

Ideal Gas Law Calculations----------

TIP: 

PV = nRT problems don't typically have a "situation 1" and "situation 2" occurring.  There's usually just one situation.

"Before / After" type problems usually require Boyle's Law, Charles' Law, Avogadro's Law, Gay-Lussac's Law, or the Combined Gas Law.

Let's try some!...

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Charles' Law Example

ex:  A sample of methane gas with a volume of 38 mL at 5°C is heated to 86°C at constant pressure.  Calculate its new volume.
_________
answer:

➞  V1 = 38 mL  ,  T1 = 5 + 273 = 278 K

➞  V2 = ?? mL  ,  T2 = 86 + 273 = 359 K

Charles' Law Example

... How come it wasn't necessary to convert V1 and V2 into liters (L) ?

Because "R" (in PV = nRT) is equal to 0.0821 L.atm / K.mol, but "R" is not being used in Charles' Law !!  :-)

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Combined Gas Law Example

ex:  Diborane gas (B2H6) has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L.  If conditions change such that the temperature is 36°C and the pressure is 468 torr, what will be the volume of the sample?
_________
answer:

situation 1:
   P1 = 345 torr
   T1 = -15 + 273 = 258 K
   V1 = 3.48 L

situation 2:
   P2 = 468 torr
   T2 = 36 + 273 = 309 K
   V2 = ?? L

➞  we'll use the Combined Gas Law,
     
      P1V1 / T1  =  P2V2 / T2

      V2 = 3.07 L  B2H6

Combined Gas Law Example==========

Ideal Gas Law Practice Problem

ex:  A gaseous sample contains 0.35 moles of Argon at a temperature of 13°C and a pressure of 568 torr.  If it's heated to 56°C and a pressure of 897 torr, calculate the change in volume that occurs.
_________
answer:

➞  this one's tricky because at first we see two pressures...

However,  n1 = n2 = remains unchanged and we're asked to find the change in volume (ΔV).

To find ΔV = V2 - V1, we'll need to use PV = nRT twice...

Units of the Ideal Gas Law

We will need to convert our pressures from torr to atmospheres (atm), and then set-up two separate PV = nRT equations:

      P1V1 = nRT1    and    P2V2 = nRT2

Here's the work that's involved...
 Ideal Gas Law Problems

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That's it for entry #3 from SECTION 5 - Gases.

In my next video from this Section ("Chapter"), we'll discuss Gas Stoichiometry and how to derive Molar Mass and Density from the Ideal Gas Law.