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Question

Boyle's, Charles' and Avogadro's results on the different state variables of a gas, can be combined into one "equation of state” known as the ideal gas equation, PV = nRT, where R = 8.514 J/mol-K. Consider the following situation.

A mixture of hydrogen and oxygen has volume 2000 cm3, temperature 300 K, pressure 100 kPa and mass 0.76 gms. Calculate the masses of hydrogen and oxygen in the mixture.


A

0.12 gms; 0.64 gms

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B

0.8gms; 0.68 gms

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C

0.24 gms; 0.52 gms

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D

0.16gms; 0.60 gms

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Solution

The correct option is A

0.12 gms; 0.64 gms


Suppose there are n1 moles of hydrogen and n2 moles of oxygen in the mixture. The pressure of the mixture will be -

P=(n1RTV)+(n2RTV)=(n1+n2)RTV

100×103Pa=(n1+n2)×[(8.3 JK1 mol1)(300 K)200×106m3]

(n1+n2)=0.08 mol .....(i)

The mass of the mixture is -

(n1×2 gms/mol)+(n2×32 gms/mol)=0.76 gms

(n1+16n2)=0.38 mol. ...(ii)

From (i) and (ii),

n1=0.06 mol and n2=0.02 mol

The mass of hydrogen = 0.06×2 gms=0.12 gms, and the mass of oxygen = 0.02×32 gms=0.64 gms.


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With the established results of Boyle, Charles and other contemporary savants, the study of gases had gained momentum. Gay-Lusaac, et al, observed that gases tend to combine in whole number ratios (one gram of oxygen would only combine with two grams of hydrogen to make water, etc.), which had no good explanation until Amedeo Avogadro, in a little noticed publication in1811, hypothesized -under the same pressure and temperature, equal volumes of gases would have equal number of particles. This was later verified, and eventually proved by the kinetic theory, and the hypothesis was promoted to "Avogadro's Law". Consider the following situation: A container made of conducting walls, having a volume V and weighing 100 gms, is filled with hydrogen gas up to a pressure P. There is a light piston, initially located at the far right end, which can be moved to divide the volume in parts. The piston is moved, very slowly, from right to left in such a way that the hydrogen is pushed out through a one-way valve on the left, and oxygen is pulled in through the right end via a similar valve. Doing this slowly makes sure that at any given point, the forces on the piston from either sides are balanced and add to zero. If the mass of the hydrogen-filled container was initially 104 grams, what is its mass when the piston has been moved all the way to the left wall? You can assume the system is always in thermal equilibrium with the surroundings, which is at a constant temperature T. Try and apply Avogadro's Law to the situation.


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