Question

If you put 3.00 moles of CO2 with some O2 into a 50 L gas chamber at a temperature of 32°C. What is the pressure of the O2 if the total pressure of the CO2 and the O2 combined is 3.00 atm?

___________ (use 3 sig figs)

(20 points)

Answer 1

Step-by-step explanation:

Assuming ideal gas behavior, we can use the mole fraction of O2 to calculate its partial pressure in the mixture:

Calculate the total number of moles of gas in the chamber:

n(total) = n(CO2) + n(O2) = 3.00 mol CO2 + n(O2)

Calculate the mole fraction of O2:

X(O2) = n(O2) / n(total) = n(O2) / (3.00 mol CO2 + n(O2))

Use Dalton's law of partial pressures to find the partial pressure of O2:

P(O2) = X(O2) * P(total) = X(O2) * (3.00 atm)

Use the ideal gas law to find the volume of the gas mixture:

PV = nRT

V = n(total) * RT / P(total) = (3.00 mol CO2 + n(O2)) * (0.0821 L·atm/(mol·K)) * (305 K) / (3.00 atm)

Substitute the values found in steps 2, 3, and 4 into the equation from step 3 to get the pressure of O2:

P(O2) = (n(O2) / (3.00 mol CO2 + n(O2))) * (3.00 atm) = (n(O2) / (3.00 mol CO2 + n(O2))) * (3.00 mol CO2 + n(O2)) * (0.0821 L·atm/(mol·K)) * (305 K) / ((3.00 mol CO2 + n(O2)) * 50 L)

P(O2) = 0.0415 atm

Therefore, the pressure of O2 in the chamber is 0.042 atm (rounded to 3 significant figures).