Question

Calculate the temperature at which $28{\text{ g}}$ ${{\text{N}}_{\text{2}}}$ occupies a volume of $10{\text{ litre}}$ at $2.46{\text{ atm}}$-
A. $300{\text{ K}}$
B. $320{\text{ K}}$
C. $340{\text{ K}}$
D. $280{\text{ K}}$

Answer 1

Hint: Temperature is the measure of the degree of warmness of any body. We are provided with mass, volume and pressure of a gas. Thus, we can use the ideal gas equation to calculate the temperature. Initially convert the nitrogen to the number of moles of nitrogen.

Complete step by step answer:
Calculate the number of moles of ${{\text{N}}_{\text{2}}}$ in $28{\text{ g}}$ ${{\text{N}}_{\text{2}}}$ as follows
The mass of any substance present in one mole of it is equal to its molar mass. Thus,
${\text{1 mol }}{{\text{N}}_{\text{2}}} = 28{\text{ g }}{{\text{N}}_2}$
Thus, the number of moles of ${{\text{N}}_{\text{2}}}$ in $28{\text{ g}}$ ${{\text{N}}_{\text{2}}}$ is ${\text{1 mol}}$.
Calculate the temperature using the ideal gas equation as follows
The relationship between volume, temperature, pressure and the amount of gas is combined into the ideal gas law. The ideal gas is also known as the general gas equation. The temperature is directly proportional to the pressure and volume and inversely proportional to the amount of the gas.
We know the ideal gas equation is,
$PV = nRT$
Where, $P$ is the pressure of the ideal gas,
$V$ is the volume of the ideal gas,
$n$ is the number of moles of ideal gas,
$R$ is the universal gas constant having a constant value $0.082{\text{ litre atm/K mol}}$
$T$ is the temperature of the gas.
Rearrange the ideal gas equation for the temperature as follows:
$T = \dfrac{{PV}}{{nR}}$
Substitute $2.46{\text{ atm}}$ for the pressure, $10{\text{ litre}}$ for the volume, $1{\text{ mol}}$ for the number of moles, $0.082{\text{ litre atm/K mol}}$ for the universal gas constant and calculate the value of temperature. Thus,
$T = \dfrac{{2.46{\text{ atm}} \times 10{\text{ litre}}}}{{1{\text{ mol}} \times 0.082{\text{ litre atm/K mol}}}}$
$T = 300{\text{ K}}$
Thus, the temperature is $300{\text{ K}}$.
Thus, the temperature at which $28{\text{ g}}$ ${{\text{N}}_{\text{2}}}$ occupies a volume of $10{\text{ litre}}$ at $2.46{\text{ atm}}$ is $300{\text{ K}}$.

Thus, the correct option is option (A).

Note:
The value of temperature can be expressed in four different units that are kelvin, Celsius, Fahrenheit and Rankine. The unit Rankine is not used very often. $300{\text{ K}}$ in terms of Celsius is $300 - 274 = {27^ \circ }{\text{C}}$.