Question

A 1 mole, 293 K gas expands isothermally, starting at 22.4 L in volume. What is its final volume? Only solve with variables, not numarically.

Answer 1

We know the ideal gas equation,

PV = nRT   ................................(1)

Where, P is pressure

V is volume

n is number of moles of gas

R = 8.314 J/mol-K is universal gas constant

T is absolute temperature

Isothermal Process : in this process the temperature of the system does not change. i.e.

or,

or,

So, for isothermal expansion, if number of moles of a gas in a system is not changing then we can modify ideal gas equation as :

  

or,

or,    ...............................(2)

For the given question, we can calculate the initial pressure of the gas using ideal gas equation.

Given initial parameters are,

Temperature (T_initial) = 293 K

Number of moles = 1 mol

Volume (V_initial) = 22.4 L = 0.0224 m³

So,   

or,

or,

So, final volume can be calculated by

  

or,

but, if the expansion is isothermal, you need the final pressure if you want to calculate the final volume using equation (2).

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