Question

Gaseous ethane can be used as a fuel for campers. A company manufactures compressed gaseous ethane in 400 ${cm}^3$ meta canisters. A typical metal canister at room temperature contains compressed gaseous ethane at a pressure of 4.00 atm.
(i)Suggest a reason why gaseous ethane in the metal canister does not behave like an ideal gas.
(ii)One metal canister is used for heating water and the pressure decreases from 4.00 atm to 1.50 atm. Assuming that the compressed ethane behaves ideally, calculate the mass of water at room temperature that could be brought to boiling if the process is 80% efficient. The enthalpy change of combustion of ethane is-1420 KJ ${mol}^{-1}$.

Answer 1

$\left(i\right)$ Since in the consiten the gases has comprased, so have intormolecular forces comes into picture, while in case of ideal gass so intermolecular forces interactions are present.

Therefore the comparessed gas behaves non ideally.

$\left(ii\right)P_i=4.0atm,V_i=400\times {10}^{-5}lt;n_i=\frac{PV}{RT}=0.065$

$\downarrow$

$P_f=1.50atm,V_f=400\times {10}^{-3}lt$

$\therefore$ Applying gas law

$\frac{n_i}{P_i}=\frac{n_f}{P_f}$

$\Rightarrow n_f=n_i\times \frac{1.5}{4}=\frac{4\times 400\times {10}^{-3}}{0.0821\times 298}\times \frac{1.5}{4}$

$=0.0245$

moles of ethan used $=n_i-n_f=0.065-0.0245$

$=0.041$

$\therefore$ Heat total released on combstion $=0.041\times 1420KJ$

$=58KJ$

Now, $Q=ms\Delta T$

$\Rightarrow 58\times {10}^3=m\times 4.2\times (100-25)\{\because S_{water}=4.2J/gm\}$

$\Rightarrow m=184gm$