Answer to Question #256857 in Chemistry for MCC

Question

A tank contains 78.0 g of N₂ and 42.0 g of Ne at a total pressure of 3.75 atm and a temperature of 50.0°C. Calculate the following quantities.

(a) moles of N₂

(b) moles of Ne

(c) the partial pressure of N₂

(d) the partial pressure of Ne

Answer 1

Solution:

The molar mass of N₂ is 28.0134 g/mol

The molar mass of Ne is 20.1797 g/mol

Calculate the moles of each gas:

(a): (78.0 g N₂) × (1 mol N₂ / 28.0134 g N₂) = 2.7844 mol N₂ = 2.78 mol N₂

Moles of N₂ = 2.78 mol

(b): (42.0 g Ne) × (1 mol Ne / 20.1797 g Ne) = 2.0813 mol Ne = 2.08 mol Ne

Moles of Ne = 2.08 mol

Dalton's law of partial pressures can be used.

Dalton's law can be expressed using the mole fraction of a gas, x: P_gas1 = x_gas1 × P_Total

The mole fraction (x) of a gas is the number of moles of that gas divided by the total moles of gas in the mixture:

x_gas1 = mole fraction of gas 1 = (Moles of gas 1) / (Total moles of gas)

Total moles of gas = Moles of N₂ + Moles of Ne = 2.78 mol + 2.08 mol = 4.86 mol

Calculate the mole fraction of each gas:

x_N2 = (Moles of N₂) / (Total moles of gas) = (2.78 mol) / (4.86 mol) = 0.572

x_N2 = 0.572

x_Ne = (Moles of Ne) / (Total moles of gas) = (2.08 mol) / (4.86 mol) = 0.428

x_Ne = 0.428

Calculate the partial pressure of each gas:

(c): P_N2 = x_N2 × P_Total = 0.572 × 3.75 atm = 2.145 atm

The partial pressure of N₂ = 2.145 atm

(d): P_Ne = x_Ne × P_Total = 0.428 × 3.75 atm =1.605 atm

The partial pressure of Ne = 1.605 atm

Answers:

(a): Moles of N₂ is 2.78 mol

(b): Moles of Ne is 2.08 mol

(c): The partial pressure of N₂ is 2.145 atm

(d): The partial pressure of Ne is 1.605 atm