A very common expression of the ideal gas law uses the number of moles in a sample,
n , rather than the number of molecules,
N . We start from the ideal gas law,
and multiply and divide the right-hand side of the equation by Avogadro’s number
This gives us
Note that
is the number of moles. We define the
universal gas constant as
and obtain the ideal gas law in terms of moles.
Ideal gas law (in terms of moles)
In terms of number of moles
n , the ideal gas law is written as
In SI units,
In other units,
You can use whichever value of
R is most convenient for a particular problem.
Density of air at stp and in a hot air balloon
Calculate the density of dry air (a) under standard conditions and (b) in a hot air balloon at a temperature of
. Dry air is approximately
and
.
Strategy and solution
We are asked to find the density, or mass per cubic meter. We can begin by finding the molar mass. If we have a hundred molecules, of which 78 are nitrogen, 21 are oxygen, and 1 is argon, the average molecular mass is
, or the mass of each constituent multiplied by its percentage. The same applies to the molar mass, which therefore is
Now we can find the number of moles per cubic meter. We use the ideal gas law in terms of moles,
with
,
,
, and
. The most convenient choice for
R in this case is
because the known quantities are in SI units:
Then, the mass
of that air is
Finally the density of air at STP is
The air pressure inside the balloon is still 1 atm because the bottom of the balloon is open to the atmosphere. The calculation is the same except that we use a temperature of
, which is 393 K. We can repeat the calculation in (a), or simply observe that the density is proportional to the number of moles, which is inversely proportional to the temperature. Then using the subscripts 1 for air at STP and 2 for the hot air, we have
Significance
Using the methods of
Archimedes’ Principle and Buoyancy , we can find that the net force on
of air at
is
or enough to lift about 867 kg. The mass density and molar density of air at STP, found above, are often useful numbers. From the molar density, we can easily determine another useful number, the volume of a mole of any ideal gas at STP, which is 22.4 L.
Check Your Understanding Liquids and solids have densities on the order of 1000 times greater than gases. Explain how this implies that the distances between molecules in gases are on the order of 10 times greater than the size of their molecules.
Density is mass per unit volume, and volume is proportional to the size of a body (such as the radius of a sphere) cubed. So if the distance between molecules increases by a factor of 10, then the volume occupied increases by a factor of 1000, and the density decreases by a factor of 1000. Since we assume molecules are in contact in liquids and solids, the distance between their centers is on the order of their typical size, so the distance in gases is on the order of 10 times as great.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills