Question

State the equation corresponding to 8g of $ {{\text{O}}_2} $ is:
(A) $ PV = 8RT $
(B) $ PV = \dfrac{{RT}}{4} $
(C) $ PV = RT $
(D) $ PV = \dfrac{{RT}}{2} $

Answer 1

Hint: We need to investigate the number of moles contained in the particular mass of oxygen. The number of moles can be determined by the mass of the substance present divided by the molar mass of the element.

Formula used: In this solution we will be using the following formula;
 $ PV = nRT $ where $ P $ is the pressure of the gas, $ V $ is the volume of the container, $ n $ is the number of moles of the gas, $ R $ is the universal gas constant, and $ T $ is the absolute temperature (temperature on Kelvin scale) of the gas.
 $ n = \dfrac{m}{M} $, where $ m $ is the mass of the substance, and $ M $ is the molar mass of the element.

Complete step by step answer
In general, according to Boyle and Charles, the pressure, temperature, volume and the number of moles of a gas are related to each other and are independent of the type of gas.
Boyle stated that the pressure of a gas is inversely proportional to the volume of the gas provided that the temperature is kept constant.
Charles’s law states that the volume of a gas is proportional to the absolute temperature provided that the gas is kept at a constant pressure.
These laws combine to form the ideal gas law given as
 $ PV = nRT $ where $ P $ is the pressure of the gas, $ V $ is the volume of the container, $ n $ is the number of moles of the gas, $ R $ is the universal gas constant, and $ T $ is the absolute temperature of the gas.
To state the equation of 8g of oxygen molecule, we find the number of moles contained. Number of moles is given as
 $ n = \dfrac{m}{M} $, where $ m $ is the mass of the substance, and $ M $ is the molar mass of the element.
Hence,
 $ n = \dfrac{8}{{16}} = \dfrac{1}{2} $ moles.
Hence, inserting into the ideal gas equation, we have
 $ PV = \dfrac{{RT}}{2} $

Thus, the correct option is D.

Note
The ideal gas law as the name implies is an idealized law. In actuality, there are no ideal gases, and the pressure, volume and temperature of a gas does depend on the type of gas. However, at low temperatures and pressures (like atmospheric pressure), gases can be approximated as ideal to a very high accuracy. Hence, the popular use of ideal gas law.