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A gas is filled in a vessel at a certain temperature and at a preesure of 80cm of mercury. At the same T more gas is filled in the vessel so that its mass increases by 60% Determine the resultant pressure in vessel?
Verified Answer
A gas is filled in a vessel at a certain temperature and at a preesure...
Ans.

Method to Solve :

P1 = 76 mmHg

P2 = ?

T1 = T2 = T

Let initial mass of the gas be m1

Increase in mass ∆m/m1 = 0.5

Thus final mass m2 = m1 + 0.5m1 = 1.5m1

Let M be the molecular mass of the gas

Thus, number of moles in the original mass of gas n1 = m1/M

Final number of moles in the gas n2 = m2/M = 1.5n1

Now eqn. of state of the gas in the initial state

P1V= n1 RT ---1.

Eqn. of state in the final state

P2V = n2 RT ---2.

By eqn. 1 and 2

P1 /n1 = P2 /n2

=> P2  = P1 (n2 /n1)

=> P2 = 76 (1.5n1/n1 )

=> P2 = 76�1.5

=> P2 = 114 mm Hg

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Most Upvoted Answer
A gas is filled in a vessel at a certain temperature and at a preesure...
Given information:
- Original pressure of gas in the vessel: 80 cm of mercury
- Mass of gas in the vessel increases by 60%

Steps to determine the resultant pressure:

Step 1: Understanding the relationship between pressure and mass:
- According to Boyle's Law, at constant temperature, the pressure of a gas is inversely proportional to its volume.
- Since the volume of the vessel remains constant, we can assume that the pressure is directly proportional to the mass of gas in the vessel.

Step 2: Calculating the mass increase:
- If the original mass of the gas in the vessel is 'm', then the mass after the increase is 60% more, which can be calculated as:
- Increased mass = m + 0.6m = 1.6m

Step 3: Calculating the pressure increase:
- Since the mass and pressure are directly proportional, we can set up the following proportion:
- Original pressure / Original mass = Resultant pressure / Increased mass
- Plugging in the given values:
- 80 cm Hg / m = Resultant pressure / 1.6m

Step 4: Solving for the resultant pressure:
- Cross-multiplying the equation from Step 3, we get:
- Resultant pressure = (80 cm Hg * 1.6m) / m
- Resultant pressure = 128 cm Hg

Final Answer:
The resultant pressure in the vessel is 128 cm of mercury.
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A gas is filled in a vessel at a certain temperature and at a preesure of 80cm of mercury. At the same T more gas is filled in the vessel so that its mass increases by 60% Determine the resultant pressure in vessel?
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