Tips for calculating the partial volume of a gas –

Por Aprende

This text proposes tips for calculating the partial volume of a gas. It is worth remembering that the partial volume of a gas is the space that a gas occupies inside a container, when the total pressure of the gas mixture is being exerted on it.

O calculating the partial volume of a gas can take into account several variables, such as:

  • The amount of matter in the gas;

  • The amount of matter in the gas mixture;

  • The total pressure of the gas mixture;

  • The total volume of the gas mixture;

  • The fraction in quantity of gas matter;

  • The temperature of the gas mixture in Kelvin.

Follow now tips for calculating the partial volume of a gasin which we use all the variables proposed above:

→ 1st Tip: Formulas

Vt = VA + VB + VC + …

VA = XA
Vt

XA = nA
nt

VA = nA
Vt nt

nA = mA
BAD

nt = nA + nB + nC + …

PA = VA
Pt Vt

→ 2nd Tip

When the exercise requires partial volume calculation but provides partial pressures of the gases in the mixture:

  • A fundamental item that the exercise will provide, in addition to partial pressures, is the volume of the system;

  • The partial pressures provided must be added to find the total system pressure (Pt):

Pt = PA + PB + PC

PA = VA
Pt Vt

Example: A mixture is formed by the gases CO, Otwo and OStwo, in a container whose volume is 5L. Each gas contained in the container has the following partial pressure, respectively: 0.50 atm, 0.20 atm and 0.30 atm. Calculate the partial volumes for each of the components of this gas mixture.

1st Step: Add the partial pressures (0.50 atm, 0.20 atm and 0.30 atm) of the three supplied gases (CO, O2 and SO2):

Pt = PCO + PO2 + PSO2

Pt = 0.5 + 0.2 + 0.3

Pt = 1 atm

2nd Step: Calculate the partial volume of CO using the total volume (5L), its partial pressure (0.5 atm) and the total pressure (1 atm) in the expression:

PCO = VCO
Pt Vt

0.5 = VCO
15

1.VCO = 0.5.5

VCO = 2.5 L

3rd Step: Calculate the partial volume of O2 using the total volume (5L), its partial pressure (0.2 atm) and the total pressure (1 atm) in the expression:

PO2 = VO2
Pt Vt

0.2 = VO2
1 5

1.VO2 = 0.2.5

VO2 = 1 L

4th Step: Calculate the partial volume of SO2 using the total volume (5L), its partial pressure (0.2 atm) and the total pressure (1 atm) in the expression:

PSO2 = VSO2
Pt Vt

0.3 = VSO2
1 5

1.VSO2 = 0.3.5

VSO2 = 1.5 L

→ 3rd Tip

Calculation of the partial volume of a gas using molar percentages:

  • In this type of situation, the exercise provides the total pressure, molar percentages of gases and the total volume of the system;

  • The molar percentages provided are the fractions in quantity of matter of each gas. To use them in calculations, simply divide by 100;

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  • The formula indicated to determine the partial volume of the gas is as follows:

VA = XA
Vt

Example: Air is a mixture of gases. More than 78% of this mixture is nitrogen. Oxygen makes up about 21%. Argon, 0.9%, and carbon dioxide, 0.03%. The rest is made up of other gases. The volume occupied by oxygen in this mixture, in a 10 L environment, is equal to?

1st Step: transform the percentage of oxygen gas (O2) into a mole fraction by dividing the given value by 100:

XO2 = 21
100

XO2 = 0.21

2nd Step: use the total volume (33.6L) and the fraction in quantity of O2 matter (0.21) in the expression:

VO2 = XO2
Vt

VO2 = 0.21
10

VO2 = 10. 0.21

VO2 = 2.1 L

→ 4th Tip

When the exercise reports volumes, temperatures and pressures of each gas and then says that they have been mixed and begin to exert a new pressure.

  • In this case, we have volume, pressure and temperature of each gas individually;

  • The exercise will inform the pressure that the mixture of these gases exerts at a new temperature;

  • The number of moles of each gas (nA) must be calculated using its pressure, volume and temperature (in Kelvin) in the Clapeyron expression:

PA.VA = nA.RT

After calculating the number of moles of each gas, it is necessary to add them together to determine the total number of moles (nt):

nt = nA + nB + …

With the number of moles, we must determine the total volume through the total pressure of the container and the temperature, also in the Clapeyron equation

Pt.Vt = nt.RT

At the end we will have enough data to calculate the partial volume of each gas (VA) using its mole number (nA), total mole number and total volume in the expression below:

VA = nA
Vt nt

Example: A volume of 8.2 L of hydrogen gas at 227°C, exerting a pressure of 5 atm, and a volume of 16.4 L of nitrogen gas, at 27°C and 6 atm, are transferred to another container kept at a constant temperature of -73ºC. Knowing that the mixture now exerts a pressure of 2 atm, calculate the volume of the container and the partial volumes of each gas. Data: R=0.082 atm.L.mol-1.K-1

1st Step: calculate the number of moles of each gas using volume, temperature (in Kelvin; just add the given value to 273) and pressure:

PH2.VH2 = nH2RT

5.8.2 = nH2.0.082.500

41 = nH2.41

nH2 = 41
41

nH2 = 1 mole

PN2.VN2 = nN2RT

6,16.4 = nN2.0,082,300

98.4 = nN2.24.6

nN2 = 98.4
24.6

nN2 = 4 mol

2nd Step: Determine the total mole number using the mole numbers of the gases found in step 1:

nt = nH2 + nN2

nt = 1 + 4

nt = 5 mol

3rd Step: Calculate the volume of the container where the mixing was carried out. To do this, we will use the sum of the mole numbers of the gases found in steps 1 and 2, the total pressure provided and the temperature (-73 oC, which, in Kelvin, is 200) in the expression below:

P.Vt = nt.RT

2.Vt = 5.0,082,200

2.Vt = 82

Vt = 82
two

Vt = 41 L

4th Step: Calculate the partial volume of each gas using the total volume, the number of moles of each gas and the total number of moles:

VH2 = nH2
Vt nt

VH2 = 1
41.5

5. VH2 = 41.1

5.VH2 = 41

VH2 = 41
5

VH2 = 8.2 L

VN2 = nN2
Vt nt

VN2 = 4
41 5

5. VN2 = 41.4

5.VN2 = 164

VN 2 = 164
5

VN2 = 32.8 L

By Me. Diogo Lopes Dias