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.
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.
The correct option is B 132 gms
If you just understand that the state variables P, V and T are constant during the whole process and use the result that, the number of hydrogen molecules initially will equal the number of oxygen molecules finally, the problem is solved.
Initially:
Total mass of the hydrogen = 104 - 100 gms = 4 gms.
Molar weight of a hydrogen gas (H2)=2 gms.
∴ Number of moles of hydrogen =[massmolar weight]=2 moles.
Finally:
Since, the P-V-T conditions have not changed, the container will finally contain exactly 2 moles of oxygen, according to Avogadro’s law.
Now, molar mass of oxygen gas (O2)=16 gms.
Mass of 2 moles of oxygen gas = 32 gms.
∴ The final mass of the oxygen filled container =(100 + 32) gms = 132. gms
132 gms
If you just understand that the state variables P, V and T are constant during the whole process and use the result that, the number of hydrogen molecules initially will equal the number of oxygen molecules finally, the problem is solved.
Initially:
Total mass of the hydrogen = 104 - 100 gms = 4 gms.
Molar weight of a hydrogen gas (H2)=2 gms.
∴ Number of moles of hydrogen =[massmolar weight]=2 moles.
Finally:
Since, the P-V-T conditions have not changed, the container will finally contain exactly 2 moles of oxygen, according to Avogadro’s law.
Now, molar mass of oxygen gas (O2)=16 gms.
Mass of 2 moles of oxygen gas = 32 gms.
∴ The final mass of the oxygen filled container =(100 + 32) gms = 132. gms
