A student collected a sample of nitrogen gas by the displacement of water as sho

Question

A student collected a sample of nitrogen gas by the displacement of water as shown by this diagram. The relevant data are given in the table below. Calculate the partial pressure of die nitrogen gas that is collected. Calculate the number of moles of nitrogen gas collected. Calculate the number of moles of water vapor in the sample. Calculate the number of molecules of water vapor in the sample. Calculate the ratio of the average speed of the nitrogen molecules to the average speed of the water molecule in the sample. Which of the two gases, N_2. or H_2O, deviates more from ideal behavior? Justify your response.

Explanation / Answer

Solution :-

Volume of sample = 2.4 L

Temperature = 33 C + 273 = 306 K

Vapor pressure of water = 32 mmHg

Total pressure = 750 mmHg

1)Calculating the partial pressure of the nitrogen gas that is collected

Partial pressure of N2 = total pressure - vapor pressure of H2O

                                        = 750 mmHg -32 mmHg

                                        = 718 mmHg

2) moles of N2 gas collected

PV= nRT

PV/RT = n

(718 mmHg * 1 atm / 760 mmHg)*2.4 L / 0.08206 L atm per mol K * 306 K = n

0.09029 mol = n

So moles of N2 collected = 0.09029 mol

3) moles of water vapor in sample

(32 mmHg * 1 atm / 760 mmHg)*2.4 L / 0.08206 L atm per mol K * 306 K = n

0.004024 mol H2O = n

So moles of water vapor = 0.004024 mol

4) molecules of water vapor

0.004024 mol H2O * 6.02*10^23 molecules / 1 mol = 2.42*10^21 molecules of water vapor

5) ratio of the speed of the nitrogen to speed of water

Rate N2 / rate H2O = (molar mass of H2O / molar mass of N2)^0.5

                                     = 0.802

So the ratio is 0.802

6) H2O deviate more from the ideal gas

Because H2O can form hydrogen bonding which increases the intermoecualr forces between the molecules which causes the molecules to have attraction which is not the case with N2

Therefore H2O deviates more.

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