Question

At what temperature the volume of $28g$ of ${N_2}$ will be 1 liter exerting a pressure of $1atm$ ?

Answer 1

In this question we will be learning about the pressure exerted on ${N_2}$. We will also calculate the temperature of a particular gas when some pressure is exerted onto it.

Complete step by step answer:
Let us first write down what is given to us in the question,
We were given,
$W = 28g$
$P = 1atm$
$V = 1l$
$m = 28g$ where
W is weight of ${N_2}$
m is given mass of ${N_2}$
P is the Pressure being exerted
V is the given volume of the gas
We Know That,
$PV = \dfrac{w}{m}RT$
Where $R$ is $0.0821$ $litre$ $atm/K/mol$
Substituting the values we know in the above equation and bring the value we need to find to the left side of the equation we get a new equation as follows;
$T = \dfrac{{mPV}}{{w \times R}}$
$T = \dfrac{{28 \times 1 \times 1}}{{28 \times 0.0821}}$ = $12.180K$
So, the volume of $28g$ of ${N_2}$ will be 1 liter exerting a pressure of $1atm$ is $12.180K$.
And hence option D is the correct answer.

Additional Information:
What is R in the above equation?
The gas constant otherwise called the molar gas constant, all inclusive gas constant, or ideal gas constant is signified by the symbol $R$. It is identical to the Boltzmann constant, yet communicated in units of energy per temperature increase per mole. The constant is likewise a blend of the constants from Boyle's law, Charles' law, Avogadro's law, and Gay-Lussac's law.

Note:
One needs to know all the formulae related to the Pressure being exerted only then they will be able to solve the above question. They need to know the value of Gas constant $R$ so that it can be correctly substituted in the equation to be the correct output. They need to know now and where the formula should be used. One needs to remember all the units correctly before entering the formula.