A 2 L sample of N2 (g) and a 1 L sample of Ar (g), each originally at 1 atm and 0°C, are combined in a 1 L tank. If the temperature is held constant, what is the total pressure of the gases in the tank? a. 1 atm b. 2 atm c. 3 atm d. 4 atm e. 5 atm

The total pressure in the tank is 3.0 atm

Explanation:

Step 1: Data given

Volume of the N2 sample = 2.0 L

Volume of the Ar sample = 1.0 L

Temperature = 0°C

Volume of the tank = 1L

Step 2: Calculate moles of N2

p*V=n*R*T

n = (p*V) / (R*T)

⇒ with p = the pressure of N2 gas = 1.0 atm

⇒ with V = the volume of N2 = 2.0 L

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

⇒ with T = the temperature = 273.15 K

n = (1.0*2.0) / (0.08206*273.15)

n = 0.0892 moles

Step 3: Calculate moles of Ar

n = (p*V) / (R*T)

⇒ with p = the pressure of Ar gas = 1.0 atm

⇒ with V = the volume of Ar = 1.0 L

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

⇒ with T = the temperature = 273.15 K

n = (1.0*1.0) / (0.08206*273.15)

n = 0.0446 moles

Step 4: Calculate total number of moles

Tot moles = 0.0892 + 0.0446 = 0.1338 moles

Step 5: Calculate total pressure

p*V=n*R*T

p = (n*R*T) / V

⇒ with p = the total pressure = ?

⇒ with n = the number of moles = 0.1338 moles

⇒ with V = the volume in the tank = 1.0 L

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

⇒ with T = the temperature = 273.15 K

p = (0.1338 * 0.08206 * 273.15) / 1

p = 3.0 atm

The total pressure in the tank is 3.0 atm

c. 3 atm

Explanation:

First, we will use the ideal gas equation to find the moles of each gas.

N₂ (g)

P * V = n * R * T

n = P * V / R * T

n = 1 atm * 2 L / (0.082 atm. L/mol. K) * 273 K

n = 0.089 mol

Ar (g)

P * V = n * R * T

n = P * V / R * T

n = 1 atm * 1 L / (0.082 atm. L/mol. K) * 273 K

n = 0.045 mol

The total gaseous moles are 0.089 mol + 0.045 mol = 0.134 mol

Now, we will use the ideal gas equation to find the pressure of the gaseous mixture.

P * V = n * R * T

P = n * R * T / V

P = 0.134 mol * (0.082 atm. L/mol. K) * 273 K / 1 L

P = 3 atm