Hydrogen gas is filled in a balloon at 20^cir | vedclass

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Question

(A) According to Charles's Law,for a constant pressure,the volume $V$ of a gas is directly proportional to its absolute temperature $T$ $(V \propto T)

Vedclass · Accepted Answer

$0.07$

Vedclass · Answer

(A) According to Charles's Law,for a constant pressure,the volume $V$ of a gas is directly proportional to its absolute temperature $T$ $(V \propto T)$.Let $n_1$ be the initial number of moles at $T_1 = 20^\circ C = 293 \ K$ and $n_2$ be the final number of moles at $T_2 = 40^\circ C = 313 \ K$.From the ideal gas equation $PV = nRT$,since $P$ and $V$ (volume of the balloon) are constant in terms of the container capacity,but the amount of gas changes to maintain pressure,we look at the relationship $n \propto 1/T$ for a fixed volume and pressure.$\frac{n_2}{n_1} = \frac{T_1}{T_2} = \frac{293}{313}$.The fraction of gas that escapes is $\frac{n_1 - n_2}{n_1} = 1 - \frac{n_2}{n_1} = 1 - \frac{293}{313}$.$\frac{\Delta n}{n_1} = \frac{313 - 293}{313} = \frac{20}{313} \approx 0.0639$.Rounding to the nearest provided option,the fraction is approximately $0.07$.

Hydrogen gas is filled in a balloon at $20^\circ C$. If the temperature is increased to $40^\circ C$ while the pressure remains constant,what fraction of the original Hydrogen gas will escape from the balloon?

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