Question

How do you find the ideal gas constant?

Answer 1

Hint By using the ideal gas equation as: $pV=nRT$, we can find the value of the ideal gas constant by putting the values of pressure, volume, temperature and number of moles. Now solve it.

Complete step by step answer:
We know that the ideal gas equation is:
$pV=nRT$
Here p represents pressure of the gas in pascal , V represents the volume of the gas in liters, n represents the no. of moles of the gas, R is the ideal gas constant or the universal gas constant and T is the temperature of the gas in kelvin.
The equation of the ideal gas i.e. $pV=nRT$ is used in those conditions when either temperature, volume or pressure of a gas are constant or in those situations when out of the four properties i.e. pressure, volume, number of moles and temperature of the gas , three properties of a gas are given.
Now considering the statement;
We can find the ideal gas constant by using the formula as;
$\begin{aligned} & pV=nRT \\\ & R=\dfrac{pV}{nT} \\\ \end{aligned}$
If the pressure of the gas is $100\text{ kPa}$, volume of the gas is $22.4\text{ liters}$, n is $1\text{ mole}$ and temperature of the gas is $273K$. Then, the ideal gas constant R is;
$\begin{aligned} & R=\dfrac{pV}{nT} \\\ & \implies{ }\dfrac{100\times 22.7}{1\times 273}kPa\text{ }l\text{ mol}{{\text{e}}^{-1}}{{K}^{-1}} \\\ & \implies{ =8}\text{.315 }kPa\text{ }l\text{ mol}{{\text{e}}^{-1}}{{K}^{-1}} \\\ \end{aligned}$

Hence, the value of ideal gas constant is $\text{8}\text{.315 }kPa\text{ }l\text{ mol}{{\text{e}}^{-1}}{{K}^{-1}}$.

Note: Don’t get confused in the ideal and real gases. Ideal gases are those gases which obeys the gas laws at all conditions of the temperature and pressure . On the other hand, real gases are gases which obey the gas law at standard conditions of temperature and pressure i.e. at 1 atmosphere pressure and $273K$ temperature.