Question

a sample of helium behaves as an ideal gas as it is heated at constant pressure from 298 K to 358 K.

If 30 J of work is done by the gas during this process, what is the mass of the heliun sample? The universal gas constant is 8.31451 J/mol x k

Abswer in units of g

Answer 1

Work by the gas is given by the work integral
W = ∫ p dV from Vi to Vf
for constant pressure process
W = p ∫ dV from Vi to Vf
= p∙(Vf - Vi) = p∙Vf - p∙Vi

use ideal gas law to express the product of pressure and volume in terms of number of moles and temperature
p∙V = n∙R∙T
=>
W = n∙R∙Tf - n∙R∙Ti = n∙R∙(Tf - Ti)
solve for n
n = W / (R∙(Tf - Ti) )
multiply by the molar mass to get the mass (for helium M =4)
n = M∙n = M∙W / (R∙(Tf - Ti) )
= 4g/mol ∙ 30 J / (8.314472J/molK ∙ (358K - 298K) )
= 0.2406 g