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.
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product