Question

Compressed oxygen is sold at a pressure of 100 atmosphere in a cylinder of 49 litre. The number of moles of oxygen in the cylinder is:
(A) 400
(B) 100
(C) 300
(D) 200

Answer 1

Ideal gas equation relates the number of moles of any gas with the pressure, temperature and volume of the gas. The equation can be given as
$PV = nRT$
where P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = universal gas constant
T = temperature

Complete Step-by-Step Solution:
We need to find the number of moles of oxygen gas in a given vessel. We will use the ideal gas equation to find the number of moles.
- We know that the ideal gas equation relates the number of moles of any gas with the pressure, temperature and volume of the gas. The equation can be given as
$PV = nRT$
Here, pressure of the gas P = 100 atm
Volume of the gas V = 49 L
number of moles = n
Universal gas constant R = 0.0821 L atm/mol K
Temperature = 298 K
Here, the temperature of the gas is not given to us. So, we will assume that the gas is at room temperature which is ${25^ \circ }C$ or 298 K. This temperature corresponds to NTP (Normal temperature and pressure).
So, we can write the above equation as
(100)(49) = (n)(0.0821)(298)
So,
$n = \dfrac{{100 \times 49}}{{0.0821 \times 298}} = 200$
Thus, the number of moles of oxygen gas n = 200 moles.

So, the correct answer to the question is (D).

Note: Remember that here we have used L atm/mol K as the unit of universal gas constant R. This is because we want to use Liter as the unit of volume. If we use ${m^3}$ as the unit of volume, then we can use r in unit J/mol K.