A vessel has 6g of oxygen at a pressure p and temperature 400k
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Answer:
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The missing part of the question is given below.
"A small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is P/2 and temperature is 300K."
Answer : 2 grams of oxygen leaks out of the vessel.
Explanation :
Here the volume of the vessel is kept constant.
Step 1: Find the volume of the vessel.
We have been given ,
Pressure = P
Temperature = 400 K
Let us find moles of oxygen.
Mole is calculated using following formula.
Molar mass of oxygen gas is 32 /mol
So we have n = 0.188 mol.
The ideal gas equation is written as
Let us modify the equation to solve for V
Let us plug in the given values.
On solving further we get,
Let us call this equation 1.
Step 2 : Set up a new equation for V after the gas leaks out.
When the hole is made in the vessel, some of the gas leaks out .
Due to this pressure changes to
and temperature changes to
Let us assume n moles of gas are left.
The new equation for V can be written as
On further simplifying we get,
Let us call this equation 2.
Step 3 : Equate the volumes in equation 1 and 2.
We know that the volume of the vessel remains constant. Therefore we can equate equation 1 and equation 2.
P can be cancelled out.
n = 0.125 mol
Amount of gas left in the vessel is 0.125 moles.
The initial amount of gas was 0.188 moles.
Amount of gas left = 0.188 - 0.125 = 0.063 moles.
Let us convert this to grams of oxygen
Therefore we can say, 2 grams of oxygen leaks out.