Question

If $ 2 $ moles of an ideal gas at $ 546K $ occupy volume $ 44.8L $ , then pressure must be:
A) $ 2 atm $
B) $ 3 atm $
C) $ 4 atm $
D) $ 1 atm $

Answer 1

Hint: The ideal gas equation relates the terms like pressure, temperature, volume, number of moles and universal gas constant. The universal gas constant or ideal gas constant has constant value, and the other terms can be found out from the other terms by substituting in the ideal gas equation.
 $ PV = nRT $
P is pressure in atm
V is volume in litres
N is number of moles in moles
R is ideal gas constant $ 0.0821Latm{\left( {mol.K} \right)^{ - 1}} $
T is temperature in kelvin.

Complete answer:
Given gas is an ideal gas, it occupies a volume of $ 44.8L $ at $ 546K $ and the given that the gas is $ 2 $ moles. The ideal gas constant is also known as universal gas constant. It can be expressed in different units and has different values.
As the volume, temperature and number of moles were given in the units of litres, kelvins and moles. The ideal gas constant will have the value of $ 0.0821Latm{\left( {mol.K} \right)^{ - 1}} $ .
Substitute all the above values in the formula,
 $ P = \dfrac{{2 \times 0.0821 \times 546}}{{44.8}} = 2atm $
Thus, the pressure obtained is $ 2atm $ .
Option A is the correct one.

Note:
The ideal gas constant can also be expressed in Joules, so one should be careful while taking the value of ideal gas constant. The value should be taken based on the other terms in ideal gas law. The units of temperature must be in kelvins only, if it is in Celsius it should be converted into kelvins.