Question

Calculate the temperature at which $28g$ of ${N_2}$ gas will occupy a volume of $10L$ at $2.46atm$

Answer 1

Hint:
 Ideal gas law obeys all laws such as Boyle’s law, Charles’s Law, Gay Lusaac’s Law at variable pressures and temperatures. Ideal gas law is the equation for a hypothetical gas that really does not exist.

Complete step by step answer:
Ideal gas obeys all the gas laws at all temperatures and pressures.
Ideal gas law is given by the formula as follows:
$PV = nRT$
Where, $P = $ pressure of the gas,
$V = $Volume of the gas
$n = $Number of moles
$R = $Universal gas constant
$T = $Temperature
Also, $n = \dfrac{m}{{MW}}$ where $m = $ mass, $MW = $ molecular weight
In order to find the temperature we will rearrange the ideal gas equation as follows:
$PV = nRT$
Therefore, $T = \dfrac{{PV}}{{nR}}$
Given Data:
Mass of nitrogen gas $ = 28g$
Molecular weight of nitrogen $\left( {{N_2}} \right) = 2 \times 14$ (as it is diatomic we will multiply the atomic mass of nitrogen by $2$)
Thus molecular weight of nitrogen gas $ = 28$
Volume $ = 10L$
Pressure $ = 2.46atm$
$R = 0.0821$
To find: Temperature $ = ?$
Formula to be used: $T = \dfrac{{PV}}{{nR}}$
Soln:
$ \Rightarrow T = \dfrac{{PV}}{{nR}}$
Substituting the value we get,
$ \Rightarrow T = \dfrac{{2.46 \times 10}}{{\dfrac{{28}}{{28}} \times 0.0821}}$
$ \Rightarrow T = \dfrac{{2.46 \times 10}}{{1 \times 0.0821}}$
on further solving, we get
$ \Rightarrow T = \dfrac{{24.6}}{{0.0821}}$
$ \Rightarrow T = 299.63K$
The temperature at which $28g$ of ${N_2}$ gas will occupy a volume of $10L$ at $2.46atm$ is $299.63K$ .

Additional information:
Properties of ideal gas:
-It does not have any volume and its mass is very negligible.
-Ideal gas does not attract or repel others.
-Ideal gas law tends to fail at low temperatures and high pressures. This gas is not applicable for heavy gases such as refrigerants.

Note:If in the sum the volume is given in terms of liter and pressure in terms of atmosphere, then we will use gas constant as $0.0821$ . And if volume is given in terms of ${m^3}$ and pressure in terms of pascal, then we will consider gas constant to be $8.314$ .