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Question

A vessel has 6g of oxygen at pressure P and temperature of 400K. A small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is at P2 and the temperature is 300K?


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Solution

Step 1: Given information

Mass of oxygen is 6g at temperature 400K.

The final pressure is at P2and the temperature is 300K.

Step 2: To find

We have to determine how much oxygen leaks out.

Step 3: Calculation

We know the relation,

PV=mMRT...(1)

P'V=m'MRT'...(2)

Where, P is the pressure, V is the volume, m is the mass given in grams, M is the molar mass, R is the ideal gas constant, and T is the temperature in Kelvin.

By dividing (1) and (2), we get

P'P=m'mT'T

Now,

m'=P'P×TT'×m

By substituting the given values, we get

=P2P×400300×6=4g

Step 4: Calculating the mass of leaked oxygen

Calculate the mass of oxygen leaked as follows:

m=m-m'=6-4=2g

Therefore, the mass of oxygen leaked is 2g.


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