molar volume 1.1.6 text book : pages 14 - 15 2008 specifications

Molar volumeMolar volume

1.1.61.1.6

Text Book : Pages 14 - 15Text Book : Pages 14 - 15

2008 2008 SPECIFICATIONSSPECIFICATIONS

1.1.6 Moles and Gas Volumes

Calculate the amount of substance in moles using gas volumes

One mole of different gases

ONE MOLE OF ANY GAS OR VAPOUR OCCUPIES

24 dm3

. . . at room temperature and pressure

rtp = room temperature and pressure (298K and 105 Pa)

ONE MOLE OF ANY GAS OR VAPOUR OCCUPIES 24 dm3 at rtp

1. Calculate the volume occupied by 0.25 mols of carbon dioxide at rtp

1 mol of carbon dioxide will occupy a volume of 24 dm3 at rtp0.25 mol of carbon dioxide will occupy a volume of 24 x 0.25 dm3 at rtp0.25 mol of carbon dioxide will occupy a volume of 6 dm3 at rtp

MOLAR VOLUMEMOLAR VOLUME

rtp = standard temperature and pressure (298K and 105 Pa)ONE MOLE OF ANY GAS OR VAPOUR OCCUPIES 24dm3 at room temperature and pressure

ONE MOLE OF ANY GAS OR VAPOUR OCCUPIES 24dm3 at rtp

1. Calculate the volume occupied by 0.25 mols of carbon dioxide at rtp

1 mol of carbon dioxide will occupy a volume of 24 dm3 at rtp0.25 mol of carbon dioxide will occupy a volume of 24 x 0.25 dm3 at rtp0.25 mol of carbon dioxide will occupy a volume of 6.0 dm3 at rtp

2. Calculate the volume occupied by 0.08g of methane (CH4) at rtp

Relative Molecular Mass of CH4 = 12.0 + (4x1.0) = 16.0

Molar Mass of CH4 = 16.0 g mol-1

Moles = mass/molar mass 0.08g / 16.0 g mol-1 = 0.005 mols

1 mol of methane will occupy a volume of 24 dm3 at rtp0.005 mol of methane will occupy a volume of 24 x 0.005 dm3 at rtp0.005 mol of methane will occupy a volume of 0.12 dm3 at rtp

that’s 120 cm3

MOLAR VOLUMEMOLAR VOLUME

ONE MOLE OF ANY GAS OR VAPOUR OCCUPIES 24dm3 at room temperature and pressure

CALCULATING THE NUMBER OF MOLES OF A SINGLE SUBSTANCE

moles = vol / molar vol volume = moles x molar volume

molar volume= volume / moles

UNITS

volume dm3 ( litres ) or cm3molar volume 24 dm3 or 24,000 cm3

THE MOLAR VOLUMETHE MOLAR VOLUME

MOLES = volume MOLAR volume MOLES = volume MOLAR volume

Volumedm3

MOLES x 24.dm3

COVER UP THE VALUE YOU WANT AND THE METHOD

OF CALCULATION IS REVEALED

1.1.6 Tasks

Write out these Key definitions

Molar volume is . . .

Examiner tip is . . . .

Worksheets

Questions : 1, 2, 3

Exercise 1.1.6 a Calculation of the volume of a given number of moles of a gas In each case calculate the volume of the number of moles of gas stated. (Assume that all volumes are measured at room temperature and pressure and that 1 mole of gas has a volume of 24 000 cm3 under these conditions). 1 1 mole of CO2

2 0.1 moles of NH3

3 0.5 moles of C2H4

4 2 moles of SO2

5 0.12 moles of SO3

6 3.4 moles of HBr

7 0.11 moles of Cl2

8 0.0040 moles of CH4

9 10 moles of H2

10 0.45 moles of O2

11 0.0056 moles of C2H6

12 0.0090 moles of C3H8

13 0.040 moles of C2H2

14 0.123 moles of NO

15 0.0023 moles of HCl

16 8.0 moles of HBr

17 0.000010 moles of HI

18 6.0 moles of NO2

19 0.0076 moles of F2

20 3.0 moles of N2

Volumedm3

MOLES x 24.dm3

1 24000 cm3 11 134.4 cm3

2 2400 cm3 12 216 cm3

3 12000 cm3 13 960 cm3

4 48000 cm3 14 2952 cm3

5 2880 cm3 15 55.2 cm3

6 81600 cm3 16 192000 cm3

7 2640 cm3 17 0.24 cm3

8 96 cm3 18 144000 cm3

9 240000 cm3 19 182.4 cm3

10 10800 cm3 20 72000 cm3

Exercise 1.1.6 b Calculation of the number of moles of gas in a given volume of that gas In each case calculate the volume of the number of moles of gas stated. (Assume that all volumes are measured at room temperature and pressure and that 1 mol of gas has a volume of 24 000 cm3 under these conditions). 1 200 cm3 of CO2 2 500 cm3 of NH3

3 1000 cm3 of C2H4

4 2000 cm3 of SO2

5 234 cm3 of SO3

6 226 cm3 of HBr 7 256 cm3 of Cl2

8 200 cm3 of CH4

9 2000 cm3 of H2

10 2400 cm3 of O2

11 700 cm3 of C2H6

12 5600 cm3 of C3H8

13 2200 cm3 of C2H2

14 210 cm3 of NO 15 800 cm3 of HCl 16 80 cm3 of HBr 17 2 cm3 of HI 18 20000 cm3 of NO2

19 420 cm3 of F2

20 900 cm3 of N2

Volumedm3

MOLES x 24.dm3

1 8.33E-032 2.08E-023 4.17E-024 8.33E-025 9.75E-036 9.42E-037 1.07E-028 8.33E-039 8.33E-02

10 1.00E-0111 2.92E-0212 2.33E-0113 9.17E-0214 8.75E-0315 3.33E-0216 3.33E-0317 8.30E-0518 8.33E-0119 1.75E-0220 3.75E-02

0.008330.020830.04170.08330.009750.0094170.01070.008330.08330.10.029160.2330.09170.008750.03330.003330.0000830.8330.01750.0375

Exercise 1.1.6 c Calculation of the mass of a given volume of gas Calculate the mass of the volume of gases stated below. (Assume that all volumes are measured at room temperature and pressure and that 1 mol of gas has a volume of 24 000 cm3 under these conditions). 1 200 cm3 of CO2

2 500 cm3 of NH3

3 1000 cm3 of C2H4

4 2000 cm3 of SO2

5 234 cm3 of SO3

6 226 cm3 of HBr 7 256 cm3 of Cl2

8 200 cm3 of CH4

9 2000 cm3 of H2

10 2400 cm3 of O2

11 700 cm3 of C2H6

12 5600 cm3 of C3H8

13 2200 cm3 of C2H2

14 210 cm3 of NO 15 800 cm3 of HCl 16 80 cm3 of HBr 17 2 cm3 of HI 18 20000 cm3 of NO2

19 420 cm3 of F2

20 900 cm3 of N2

Volumedm3

MOLES x 24.dm3

mass

MOLES x Molar mass

1 0.00833 x 44 = 0.366522 0.02083 x 17 = 0.354113 0.0417 x 28 = 1.16764 0.0833 x 64.1 = 5.339535 0.00975 x 80.1 = 0.7809756 0.009417 x 80.9 = 0.7618357 0.0107 x 71 = 0.75978 0.00833 x 16 = 0.133289 0.0833 x 2 = 0.166610 0.1 x 32 = 3.211 0.02916 x 30 = 0.874812 0.233 x 44 = 10.25213 0.0917 x 26 = 2.384214 0.00875 x 30 = 0.262515 0.0333 x 36.5 = 1.2154516 0.00333 x 80.9 = 0.26939717 0.000083 x 127.9 = 0.01061618 0.833 x 46 = 38.31819 0.0175 x 38 = 0.66520 0.0375 x 28 = 1.05

Exercise 1.1.6 d Calculation of the volume of a given mass of gas In each case calculate the volume on cm3 of the mass of gas given. (Assume that all volumes are measured at room temperature and pressure and that 1 mol of gas has a volume of 24 000 cm3 under these conditions). 1 2 g of CO2

2 5 g of NH3

3 10 g of C2H4

4 20 g of SO2

5 2.34 g of SO3

6 2.26 g of HBr 7 10 g of Cl2

8 20 g of CH4

9 200 g of H2

10 240 g of O2

11 70 g of C2H6

12 56 g of C3H8

13 22 g of C2H2

14 20 g of NO 15 8 g of HCl 16 8 g of HBr 17 2 g of HI 18 23 g of NO2

19 42 g of F2

20 90 g of N2

mass

MOLES x Molar mass

Volumedm3

MOLES x 24.dm3

1 1090

2 7050

3 85700

4 7490

5 701

6 670

7 3380

8 30000

9 2400000

10 180000

11 56000

12 30500

13 20300

14 16000

15 5260

16 2370

17 375

18 12000

19 26500

20 77100

Exercise 1.1.6 e Calculation of the Relative Molecular Mass of a gas from mass and volume data for the gas In each case you are given the mass of a certain volume of an unknown gas. From each set of data calculate the Relative Molecular Mass of the gas. (Assume that all volumes are measured at room temperature and pressure and that 1 mol of gas has a volume of 24 000 cm3 under these conditions). 1 0.373 g of gas occupy 56 cm3

2 0.747 g of gas occupy 280 cm3



















mass

MOLES x Molar mass

Volumedm3

MOLES x 24.dm3

1 159

2 64

3 80

4 71

5 2

6 28

7 30

8 58.1

9 32

10 27.9

11 34.03

12 16.97

13 38.02

14 27.98

15 43.97

16 31.92

17 210.96

18 36.48

19 81.12

20 128.06

1.1.6 - Gas Calculation Worksheet 1. Why is the volume occupied by one mole of any gas at 25 oC and 100 kPa. 24 dm3 ? 2. Calculate the volume that 0.2 moles of a gas occupy 3. Calculate the volume that 0.5 moles of a gas occupy 4. Calculate the mass of a sample of carbon dioxide which occupies 20 dm3 at 25 oC

and 100 kPa. 5. Calculate the relative molecular mass of a gas if a 500 cm3 sample at 25 oC and 1 atm

has a mass of 0.66 g. 6. At 25 oC and 100 kPa a gas balloon occupies a volume of 20 dm3.

Will the mass of the gas change if a) the volume is decreased to 10 dm3 by compressing it b) the pressure outside the balloon is decreased to 50 kPa

7. 10.0 g of calcium nitrate is heated until it fully decomposes. Calculate

a) the volume of nitrogen dioxide evolved b) the volume of oxygen evolved c) the total volume of gas evolved

Equation: 2Ca(NO3)2(s) 2CaO(s) + 4NO2(g) + O2(g) 8. Calculate the volume of oxygen produced at 298 K and 100 kPa by the

decomposition of 30 cm3 of 0.1 moldm-3 hydrogen peroxide. Equation: 2H2O2(aq) 2H2O(l) + O2(g) 9. Lead (IV) oxide dissolves in concentrated hydrochloric acid according to the

following equation: PbO2(s) + 4HCl(aq) PbCl2(s) + Cl2(g) + 2H2O(l)

Starting with 37.2 g of lead (IV) oxide, calculate: a) the volume of 12 moldm-3 HCl needed to completely dissolve it b) the mass of PbCl2 produced c) the volume of chlorine produced at 298 K and 100 kPa. 10. What mass of magnesium, and what volume of 2.0 moldm-3 hydrochloric acid,

will be required to produce 100 cm3 of hydrogen gas at 298 K and 100 kPa? Equation: Mg(s) + 2HCl(aq) MgCl2(aq) + H2(g) 11. 0.52 g of sodium was added to 100 cm3 of water. Calculate: a) The volume of hydrogen evolved at 298 K and 100 kPa

b) The concentration of the sodium hydroxide solution produced, assuming the volume of water does not change.

Equation: 2Na(s) + 2H2O(l) 2NaOH(aq) + H2(g)

Volumedm3

MOLES x 24.dm3

mass

MOLES x Molar mass

R is the gas constant ( 8.314472(15) J K-1 mol-1 )

So what is the molar volume of a gas ? . .rearrange and calculate !The unit can be cm3 or dm3

p is the pressure – Pa . . . that’s actually – 101,325 Nm-2

V is the volume – m3 . . . . that’s 100 x 100 x 100 cm3 n is the number of moles of gas – that just 1T is the temperature measured in Kelvin – rtp is 298K

Extension . . Why . . .

Combined and ideal gas laws

p V = n R T

V = 8.314472 x 1 x 298 101,325

= 0.0244531

X1,000,000 ( convert to cm3)

= 24, 453 cm3

That's about 24.5 dm3

p V = n R T V = n R Tp

Volumedm3

MOLES x 24.dm3

Volumedm3

MOLES x 24.dm3

mass

MOLES x Molar mass

mass

MOLES x Molar mass

7. 10.0 g of calcium nitrate is heated until it fully decomposes. Calculate

a) the volume of nitrogen dioxide evolved b) the volume of oxygen evolved c) the total volume of gas evolved

Equation: 2Ca(NO3)2(s) 2CaO(s) + 4NO2(g) + O2(g) Ca(NO3)2 = 164

10/164 = 0.061 Vol NO2 = 4 x 0.061 x 24 = 2.93 Vol O2 = 0.5 x 0.061 x 24 = 0.732

molar volume 1.1.6 text book : pages 14 - 15 2008 specifications

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