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Question

Equal moles of hydrogen and oxygen gases are placed in a container with a pin-hole through which both can escape. What fraction of the oxygen escapes in the time required for one-half of the hydrogen to escape?


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Solution

Step 1: Analyse the formula.

Assume one mole of Hydrogen (H) and one mole of Oxygen (O) gases are placed in a container with a pin-hole through which both can escape.

nOtHnHtO=MHMO

Here, nO represents the number of moles of oxygen effused in timetO and MO is the molar mass of oxygen.

Similarly, nH represents the number of moles of hydrogen effused in time tH and MH is the molar mass of hydrogen.

Step 2: Find the fraction of Oxygen escaped.

According to the question, one-half of the Hydrogen has escaped.

The molar mass of Oxygen gas and Hydrogen gas is 32gmol-1 and 2gmol-1

Also, tO is equal to tH, according to the question.

So, substituting these values in the formula, we get

:nOtHnHtO=MHMOnO12=232

So, nO=12×14=18

Thus, the fraction of the oxygen that escapes in the time required for one-half of the hydrogen to escape is 18


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