Question

Find the universal gas constant given that one litre of oxygen weighs 1.429gm. Pressure P=$1.013\times {{10}^{5}}N{{m}^{-2}}$. Molecular weight of oxygen is 32.

Answer 1

Hint: Let us find the number of moles of oxygen first. Number of moles is equal to the ratio of mass of oxygen to that of the molecular weight of the oxygen. Also, we need to convert the volume in litres to a meter cube. The temperature at normal condition is equal to ${{20}^{0}}C$. The temperature must be converted to kelvin too.
Formula used:
$\begin{align}
  & n=\dfrac{w}{molar \, mass} \\
 & PV=nRT \\
\end{align}$

Complete answer:
Let us first do the unit conversions for temperature, volume and find the number of moles of oxygen molecule,
$\begin{align}
  & T={{20}^{0}}C \\
 & T=273+{{20}^{0}}C \\
 & \Rightarrow T=293K \\
 & \Rightarrow V={{10}^{-3}}{{m}^{3}} \\
\end{align}$
Next, let's find the number of moles,
$\begin{align}
  & n=\dfrac{1.429}{32} \\
 & n=0.04465 \\
\end{align}$
The pressure, temperature, number of moles and the volume is known, let us find the universal gas constant,
$\begin{align}
  & PV=nRT \\
 & \Rightarrow R=\dfrac{PV}{nT} \\
 & \Rightarrow R=\dfrac{1.1013\times {{10}^{5}}\times {{10}^{-3}}}{0.44\times 293} \\
 & \Rightarrow R=0.8542Jmo{{l}^{-1}}{{K}^{-1}} \\
\end{align}$
In this way, we can find the value of the universal gas constant by substituting certain values after converting them to the same units.

Additional Information:
The ideal gas law is a physical law describing the relationship of the measurable properties of an ideal gas like the pressure, temperature and the volume. It is derived by combining certain individual laws like Boyle's law, Charles law etc. It is also called the general gas equation. It is used to approximate the behaviour of different gases at certain controlled conditions. This ideal gas equation was first stated by emile Clapeyron in the year 1834. This law can also be derived from microscopic kinetic theory.

Note:
Units play an important role in the ideal gas law formula. Most of us use the volume in litres and the temperature in Celsius. But, the standard units to be used are metric cube and the kelvin. These are all taken in SI units. So, be sure all the units are in either SI, CGS or MKS system of measurement.