Question

A gas occupies a volume of (5 , textdm^3) at (2 , textatm) and (273 , textK). Calculate the number of moles present in the gas.

a) 0.5 moles
b) 1 mole
c) 2 moles
d) 4 moles

Answer 1

Using the Ideal Gas Law with the given values (2 atm, 5 L, 273 K), we determine that the gas has approximately 0.446 moles. The closest answer choice to this calculation is 0.5 moles. The correct option is a.

Step-by-step explanation:

To calculate the number of moles present in a gas, we can use the Ideal Gas Law, which is PV = nRT. In this question, we are given the pressure (P) as 2 atm, the volume (V) as 5 dm³ (which can also be written as 5 liters), and the temperature (T) as 273 K. R is the ideal gas constant, which is approximately 0.0821 L·atm/(K·mol) when pressure is in atmospheres and volume is in liters.

Using this information, we can rearrange the Ideal Gas Law to solve for n (the number of moles): n = PV / (RT). Substituting in the known values and solving for n gives us n = (2 atm × 5 L) / (0.0821 L·atm/(K·mol) × 273 K) = 10 atm·L / (22.4173 L·atm/mol) ≈ 0.446 moles.

Therefore, the correct answer is (a) 0.5 moles, which is the closest option provided.