Question

How many moles of a gas occupy a 3.45 L container at pressure of 150 kPa and temperature of ${{45.6}^{\circ }}C$ ?

Answer 1

Hint:The ideal gas law is the equation of state for an ideal gas (hypothetical). It is a good approximation of the behavior of many gases under certain conditions. It is a combination of the empirical Charles's law, Boyle's law, Avogadro's law, and Gay-Lussac's law.

Formula used: ideal gas equation (equation of state):
$PV=nRT$

Complete step-by-step answer: The empirical relationship between volume, the temperature, the pressure, and the amount of a gas can be combined into the ideal gas law which can be written as follows:-
$PV=nRT$
Where,
P = pressure of the gas
V =volume of gas it occupies
n = number of moles of gas present in the solution or sample
R = universal gas constant, equal to $0.0821\dfrac{atm\cdot L}{mol\cdot K}$
T = absolute temperature of the gas
The ideal gas law helps us to calculate the value of the fourth quantity (either among P, V, T, or n) needed to describe a gaseous sample when the other three quantities are known.
Since we have the values of P, V, T, therefore we can easily calculate n by using the ideal gas equation.
Now, it is important that the units we have for the V, P, and T of the gas must match the unit used in the expression of the universal gas constant (R).
Suppose we use R= $0.0821\dfrac{atm\cdot L}{mol\cdot K}$
Then, P = 150kPa = $\dfrac{150}{101.325}atm$ (as we know $1\text{ }atm\text{ }=\text{ }101.325\text{ }kPa$ )
V = 3.45 L
T = ${{45.6}^{\circ }}C$ = (45.6+273.15)K (as we know $T[K]=T{{[}^{\circ }}C]+273.15$ )
Now, let us rearrange the formula to calculate n:-
$PV=nRT \\
\Rightarrow n=\dfrac{PV}{RT} \\
$
On substituting the given values in the above formula, we get:-
\[n=\dfrac{\dfrac{150}{101.325}atm\times 3.45L}{0.0821\dfrac{atm\cdot L}{mol\cdot K}\times (45.5+273.15)K}=0.195moles\]
 0.195 moles of a gas occupies a 3.45 L container at pressure of 150 kPa and temperature of ${{45.6}^{\circ }}C$

Note: Always remember to put values in formula according to the universal gas constant and similarly do the conversion as well of the given values. Other gas constant values which can be preferred are as follows:-
-8.314$J\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$
 -8.314${{m}^{3}}\cdot Pa\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$
-2 $cal\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$
-8.205${{m}^{3}}\cdot atm\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$
-0.082$L\cdot atm\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$