Question

A gas mixture contains 0.700 mol of N2, 0.300 mol of H2, and 0.400 mol of CH4. Calculate the pressure of the gas mixture and the partial pressure of each constituent gas if the mixture is in a 8.00 L vessel at 27.00°C

Answer 1

Answer:

Pressure of the gas mixture: 4.30 atm

Partial pressure N₂ = 2.15 atm

Partial pressure H₂ =  0.91 atm

Partial pressure CH₄ = 1.23 atm

Explanation:

To determine partial pressure we sum the total moles in order to find out the total pressure

We can work with mole fraction

We apply the Ideal Gases Law

0.700 N₂ + 0.300 H₂ + 0.400 CH₄ = 1.4 moles

We replace data  → P . V = n . R .T

T° must be at K →  27  °C + 273 = 300 K

P . 8 L = 1.4 mol . 0.082 L.atm/mol.K  . 300 K

P = ( 1.4 mol . 0.082 L.atm/mol.K  . 300 K) / 8 L = 4.30 atm (Total pressure)

We apply the mol the fraction for the partial pressure

Moles x gas / total moles = partial pressure x gas / total pressure

Mole fraction N₂ → 0.700 /1.4 = 0.5

Partial pressure N₂ = 0.5 . 4.30 atm =2.15 atm

Mole fraction H₂  →  0.300 / 1.4 = 0.21

Partial pressure H₂ = 0.21 . 4.30 atm = 0.91 atm

Mole fraction CH₄ → 0.400 /1.4 = 0.28

Partial pressure CH₄ = 0.28 . 4.30 atm =1.23 atm

Answer 2

Answer:

Partial pressure N2= 2.155 atm

Partial pressure H2 =0.922 atm

Partial pressure CH4 =1.233 atm

Total pressure is 4.31 atm

Explanation:

Step 1: Data given

Number of moles N2 = 0.700 moles

Number of moles H2 = 0.300 moles

Number of moles CH4 = 0.400 moles

Volume = 8.00 L

Temperature = 27.0 °C = 300 K

Step 2: Calculate the total moles

Total moles = Moles N2 + moles H2 + moles CH4

Total moles = 0.700 + 0.300 + 0.400

Total moles = 1.400 moles

Step 3: Calculate total pressure

p*V = n*R*T

⇒with p = the total pressure = TO BE DETERMINED

⇒with V = the volume = 8.00 L

⇒with n = the number of moles = 1.400 moles

⇒with R = the gas constant = 0.08206 L*atm/K*mol

⇒with T = the temperature = 300 K

p = (n*R*T)/V

p = (1.400 * 0.08206 * 300) / 8.00

p = 4.31 atm

Step 4: Calculate mol fraction

Mol fraction = number of moles / total moles

Mol fraction N2 = 0.700 moles / 1.400 moles = 0.500

Mol fraction H2 = 0.300 moles / 1.400 moles = 0.214

Mol fraction CH4 = 0.400 moles / 1.400 moles = 0.286

Step 5: Calculate partial pressure

Partial pressure = mol fraction * total pressure

Partial pressure N2 = 0.500 * 4.31 atm = 2.155 atm

Partial pressure H2 = 0.214 * 4.31 = 0.922 atm

Partial pressure CH4 = 0.286 * 4.31 = 1.233 atm