N₂O (laughing gas) is used as an anesthetic. A dentist has a 2.00 L flask of N₂O at a pressure of 1.00 atm and a 3.00 L flask of nitrogen gas at 2.00 atm that are separated by a valve. What is the pressure in the flasks when the valve is opened, and the gases mix together? Both flasks are at the same temperature, and the temperature does not change when the gases mix.

Question

Quizplus · Accepted Answer

We can use the ideal gas law to solve this problem: PV = nRT where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the absolute temperature. First, we need to find the number of moles of each gas in their respective flasks. For N₂O: n1 = PV/RT = (1.00 atm)(2.00 L)/(0.0821 L atm/mol K)(T) And for nitrogen: n2 = PV/RT = (2.00 atm)(3.00 L)/(0.0821 L atm/mol K)(T) Since both flasks are at the same temperature, we can set n1 = n2 and solve for T: (1.00 atm)(2.00 L)/(0.0821 L atm/mol K)(T) = (2.00 atm)(3.00 L)/(0.0821 L atm/mol K)(T) T = 296 K Now we can find the total number of moles of gas after the valve is opened: ntotal = n1 + n2 = (1.00 atm)(2.00 L)/(0.0821 L atm/mol K)(296 K) + (2.00 atm)(3.00 L)/(0.0821 L atm/mol K)(296 K) ntotal = 0.118 mol + 0.219 mol ntotal = 0.337 mol The total volume of gas is simply the sum of the individual volumes: Vtotal = V1 + V2 = 2.00 L + 3.00 L Vtotal = 5.00 L Finally, we can use the ideal gas law again to find the pressure of the mixed gases: Ptotal = ntotalRT/Vtotal = (0.337 mol)(0.0821 L atm/mol K)(296 K)/5.00 L Ptotal = 1.60 atm Therefore, the pressure in the flasks when the valve is opened is 1.60 atm, so the answer is C).

N2O (Laughing Gas) Is Used as an Anesthetic

N₂O (Laughing Gas) Is Used as an Anesthetic