Question

To an evacuated vessel with a movable piston under a total pressure of 1 atm, 0.1 mol of He and an unknown compound (vapour pressure 0.68 atm at 0℃) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0℃ is close to:
a.) 7
b.) 8
c.) 9
d.) 10

Answer 1

Hint: An ideal gas is a hypothetical gas, because it would be much easier if things like intermolecular forces do not exist to complicate the simple Ideal gas law. Ideal gases are essentially point masses moving in constant, random, straight-line motion.
Ideal gas equation: PV = nRT

Complete step by step solution:

The Ideal Gas Equation, let us state the four gas variables and one constant for a better understanding. The four gas variables are: Pressure (P), Volume(V), Number of moles(n), Temperature(T). Lastly, the constant in the equation shown below is R, known as the Gas constant.
PV = nRT
Now, as given here in the question, let’s assume the unknown compound as x and its vapour pressure is 0.68 atm.
Pressure of helium will be = 1 - 0.68 = 0.32 atm
Now according to the Ideal gas Equation:
PV = nRT
V = nRT/P
Here, P = pressure of helium, n = number of moles of Helium.
Now, V = $${\displaystyle \frac{0.1\times 0.082\times 273}{0.32}}$$ = 7 L
Therefore, from the above solution we can conclude that the total volume will be 7L, the correct option will be (a).

Note: The Ideal Gas Law is simply the combination of all Simple Gas Laws i.e. Boyle's Law, Charles' Law, and Avogadro's Law and so if you learn this one means you have learned them all. The Simple Gas Laws can always be derived from the Ideal Gas equation.