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Assuming that both gases follow the ideal gas law, we have for both gases PV=nRT where P is the pressure, V the volume, T the absolute temperature, R the gas constant, and n the number of moles.
Let subscript _1 refer to the Helium gas and _2 to the Argon gas. You can write
Divide the left sides one by the other and do the same for the right sides. Since P_1=P_2 and T_1=T_2 there are cancellations and you are left with
That is all you can say: The ratio of the volumes is equal to the ratio of the numbers of moles.
Now using the molar masses of the gases (M_1=4 g, and M_2=40 g) you find n_1 is about 2 moles and n_2 is also about 2 moles. The conclusion is that the two balloons have approximately the same volume.
Note:You can use more accurate molar masses for the gases but that will not change the conclusion.
The question should have been: What is the ratio of the volumes of the balloons?
Posted on Apr 26, 2013
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Posted on Jan 02, 2017
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