Mole and Volume
a. Ideal Gas Law
At certain temperature and pressure, then formula used is the ideal gas formula. When the values of any three of the variables P, V, T, and n are known, the value of the fourth can be calculated using the ideal gas law. The constant R in the equation is called the gas constant and has the same value for all gases.
P = pressure of the gas (atm)
V = volume of the gas (L)
n = number of moles (mole)
R = gas constant (0,0821 atm L/mol K)
T = absolute temperature (K)
Worked example
How many moles of air are in the lungs of an average adult with a lung capacity of 3.8 L? Assume that the person is at 1.00 atm pressure and has a normal body temperature of 37°C.
Strategy
This problem asks for a value of n when V, P, and T are given. Rearrange the ideal gas law to the form n = PV /RT convert the temperature from degrees Celsius to Kelvin, and substitute the given values of P, V, and T into the equation.
Solution
The lungs of an average adult hold 0.15 mol of air.
b. At Standard Temperature and pressure
The specific conditions used in the calculation—1 atm pressure and 0°C (273.15 K)—are said to represent standard temperature and pressure, abbreviated STP. These standard conditions are generally used when reporting measurements on gases.
By using the formula of ideal gas we can calculate volume of 1 mol gas as :
So we know that at STP (Standar Temperature and Pressure), volume of 1 mol gas is 22,4 L or at STP there are 22,4 L/mol gas.
The name ideal gas law implies that there must be some gases whose behavior is nonideal. In fact, there is no such thing as an ideal gas that obeys the equation perfectly under all circumstances; all real gases deviate slightly from the behavior predicted by the law. As Table 9.4 shows, for example, the actual molar volume of a real gas often differs slightly from the 22.414 L ideal value. Under most conditions, though, the deviations from ideal behavior are so slight as to make little difference.Worked Example
Calculate the number of mole of hydrogen gases which have volume 6,72 liter, if measured at 0 °C and 1 atm of pressure!
Answer :
Measured a 0o C and 1 atm means that gases is measured at STP condition.
So,,,
Mole H2 = 
= 6,72 L
22,4 L/mol
= 0,3 mole
c. Volume of Gas That Reference to Another Gas
c. Volume of Gas That Reference to Another Gas
In 1811, Amedeo Avogadro postulated that :
At the same temperature and pressure, equal volumes of all gases contain the same number of molecules.
Avogadro’s Law can also be stated as follows.
At constant temperature and pressure, the volume, V, occupied by a gas sample is directly proportional to the number of moles, n, of gas.
For two samples of gas at the same temperature and pressure, the relation between volumes and numbers of moles can be represented at constan T and P as :
Worked example
Determine volume from 2 mol nitrogen gas if measured at:
a. STP
b. T=30 °C and P=1 atm
c. At same P and T, where 0,5 mol oxygen gas have volume 15 liter
Answers :
a. At STP , Vm = 22,4 liter/mol
V = n × Vm
= 2 mol × 22,4 liter/mol
= 44,8 liter
b. T = 273 + 30 = 303 K
V = nRT/P
= 2 mol × 0,082 L atm/mol K × 303 K
1 atm
= 49,692 liter
c.
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