Answers to Ideal Gas Law Problems

Answers to ideal gas law problems

1. n = PV / RT n = [ (750.0 mmHg / 760.0 mmHg atm¯1) (0.890 L) ] / (0.08206 L atm mol¯1 K¯1) (294.0 K)

2. P = nRT / V P = [ (1.09 g / 2.02 g mol¯1) (0.08206 L atm mol¯1 K¯1) (293.0 K) ] / 2.00 L Multiply the answer (which is in atm) by 760.0 mmHg atm¯1 to get mmHg 3. V = nRT / P V = [ (3.00 mol) (0.08206 L atm mol¯1 K¯1) (297.0 K) ] / (762.4 mmHg / 760.0 mmHg atm¯1

4. V = nRT / P V = [ (20.0 g / 40.0 g mol¯1) (0.08206 L atm mol¯1 K¯1) (273.0 K) ] / (1.00 atm)

5. n = PV / RT n = [ (2.50 atm) (0.1000 L) ] / [ (0.08206 L atm mol¯1 K¯1) (298.0 K) ] 6. n = PV / RT

n = [ (2.50 atm) (37.0 L) ] / [ (0.08206 L atm mol¯1 K¯1) (353.0 K) ]

7. The volume would increase. In fact, it would double.

8. V = nRT / P

V = [ (1.27 mol) (0.08206 L atm mol¯1 K¯1) (273.0 K) ] / 1.00 atm or (22.4 L / 1.00 mol) = (x / 1.27 mol)

9. P = nRT / V P = [ (0.150 mol) (0.08206 L atm mol¯1 K¯1) (296.0 K) ] / 8.90 L

10. V = nRT / P V = [ (32.0 g / 46.0 g mol¯1) (0.08206 L atm mol¯1 K¯1) (291.0 K) ] / 3.12 atm

11. V = nRT / P V = [ 2.40 mol) (0.08206 L atm mol¯1 K¯1) (323.0 K) ] / 2.00 atm

12. n = PV / RT n = [ (60.0 atm) (7.50 L) ] / [ (0.08206 L atm mol¯1 K¯1) (308.5 K) ]

Divide 35.44 g by the number of moles calculated to get the molecular weight.

The moles of gas would be the same if the gas was switched to oxygen. Since the temperature and pressure would be the same, the same volume willcontain the same number of molecules of gas, i.e. moles of gas. This is Avogadro's Hypothesis.

This calculates the number of moles of CO2. Multiply the moles by the molecular weight of CO2 to get the grams. Under the same set of conditions, the moles of oxygen would be the same, so multiply the calculated moles by the molecular weight of O2 to get the grams.

16. V = nRT / P V = [ (2.34 g / 44.0 g mol¯1) (0.08206 L atm mol¯1 K¯1) (273.0 K) ] / 1.00 atm

17. n = PV / RT n = [ (1.00 atm) (56.2 L) ] / [ (0.08206 L atm mol¯1 K¯1) (273.0 K) ] Multiply the moles by the atomic weight of Ar to get the grams.

18. T = PV / nR T = [ (1.95 atm) (12.30 L) ] / [ (0.654 mol) (0.08206 L atm mol¯1 K¯1) ]

19. Since one mole of gas occupies 22.4 L at STP, the molecular weight of the gas is 30.6 g mol¯1

20. 11.2 L at STP is one-half molar volume, so there is 0.5 mol of gas present. Therefore, the molecular weight is 80.0 g mol¯1

21. This problem, as well as the two just above can be solved with PV = nRT. You would solve for n, the number of moles. Then you would divide the grams given by the mole calculated. Since it is at STP, we can also use a ratio method (see prob. 111) (19.2 L / 12.0 g) = (22.4 L / x )

22. n = PV / RT n = [ (700.0 mmHg / 760.0 mmHg atm¯1) (48.0 L) ] / [ (0.08206 L atm mol¯1 K¯1) (293.0 K) ]

Then, divide the grams given (96.0) by the moles just calculated above. This will be the molecular weight.

23. n = PV / RT n = [ (79.97 kPa / 101.325 kPa atm¯1) (4.167 L) ] / [ (0.08206 L atm mol¯1 K¯1) (303.0 K) ]

24. (3.00 L / 9.50 g) = (22.4 L / x )

25. (0.250 L / 1.00 g) = (22.4 L / x )

26. (0.150 L / 0.250 g) = (22.4 L / x )

27. n = PV / RT n = [ (0.890 atm) (4.50 L) ] / [ (0.08206 L atm mol¯1 K¯1) (293.5 K) ] Then, divide the grams given (1.089) by the moles just calculated above. This will be the molecular weight.

29. If 9.006 grams of a gas are enclosed in a 50.00 liter vessel at 273.15 K and 2.000 atmospheres of pressure, what is the molar mass of the gas? What gas is this? n = PV / RT n = [ (2.000 atm) (50.00 L) ] / [ (0.08206 L atm mol¯1 K¯1) (273.15 K) ]

Then, divide the grams given (9.006) by the moles just calculated above. This will be the molecular weight. The answer (2.019 g 1 mol¯ ) is approximately that of hydrogen gas, H2

30. 0.08206 L atm mol¯1 K¯1 The gas constant.

31 a. 14.0 g / 4.00 g mol¯1 = 3.50 mol b. 49.0 g / 28.0 g mol¯1 = 1.75 mol c. 3.50 mol / 5.25 mol d. 1.75 mol / 5.25 mol e. Use PV = nRT to determine the total pressure in the container.

P = nRT / V

P = [ (5.25 mol) (0.08206 L atm mol¯1 K¯1) (258.0 K) ] / 50.00 L

The total pressure times the mole fraction of He will give helium's partial pressure.

f. The total pressure times the mole fraction of N2 will give nitrogen's partial pressure. Since it is the only other value, you could subtract helium's answer from the total. g. Already done to answer part e. h. V = nRT / P

V = [ (5.25 mol) (0.08206 L atm mol¯1 K¯1) (273.0 K) ] / 1.00 atm