Calculating moles per cubic meter and liters per mole
Calculate: (a) the number of moles in
of gas at STP, and (b) the number of liters of gas per mole.
Strategy and Solution
(a) We are asked to find the number of moles per cubic meter, and we know from
[link] that the number of molecules per cubic meter at STP is
. The number of moles can be found by dividing the number of molecules by Avogadro’s number. We let
stand for the number of moles,
(b) Using the value obtained for the number of moles in a cubic meter, and converting cubic meters to liters, we obtain
Discussion
This value is very close to the accepted value of 22.4 L/mol. The slight difference is due to rounding errors caused by using three-digit input. Again this number is the same for all gases. In other words, it is independent of the gas.
The (average) molar weight of air (approximately 80%
and 20%
is
Thus the mass of one cubic meter of air is 1.28 kg. If a living room has dimensions
the mass of air inside the room is 96 kg, which is the typical mass of a human.
The density of air at standard conditions
and
is
. At what pressure is the density
if the temperature and number of molecules are kept constant?
The best way to approach this question is to think about what is happening. If the density drops to half its original value and no molecules are lost, then the volume must double. If we look at the equation
, we see that when the temperature is constant, the pressure is inversely proportional to volume. Therefore, if the volume doubles, the pressure must drop to half its original value, and
A very common expression of the ideal gas law uses the number of moles,
, rather than the number of atoms and molecules,
. We start from the ideal gas law,
and multiply and divide the equation by Avogadro’s number
. This gives
Note that
is the number of moles. We define the universal gas constant
, and obtain the ideal gas law in terms of moles.
Ideal gas law (in terms of moles)
The ideal gas law (in terms of moles) is
The numerical value of
in SI units is
In other units,
You can use whichever value of
is most convenient for a particular problem.
Calculating number of moles: gas in a bike tire
How many moles of gas are in a bike tire with a volume of
a pressure of
(a gauge pressure of just under
), and at a temperature of
?
Strategy
Identify the knowns and unknowns, and choose an equation to solve for the unknown. In this case, we solve the ideal gas law,
, for the number of moles
.
Solution
1. Identify the knowns.
2. Rearrange the equation to solve for
and substitute known values.
Discussion
The most convenient choice for
in this case is
because our known quantities are in SI units. The pressure and temperature are obtained from the initial conditions in
[link] , but we would get the same answer if we used the final values.
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?