calculation of molar fraction and pressure
Posted: Thu Aug 12, 2021 2:58 am
Hi everyone, i need your help again. I have this exercise: "In a closed reactor of 8.00 dm ^ 3, thermostated at a certain temperature, 2.50 dm ^ 3 of methane, CH4, measured at the pressure of 1.45 * 10 ^ 5 Pa, are mixed with 4.50 dm ^ 3 of oxygen, measured at 2.70 * 10 ^ 5 Pa and at the same temperature. A spark ignites the combustion of methane:
CH4 (g) + 2O2 (g) -> CO2 (g) + 2H2O (g)
calculate a) the total pressure and partial pressures of the gases before combustion; b) the molar fractions and partial pressures after combustion, knowing that at this temperature the water is in the form of vapor. "
I solved point a) like this:
I apply Boyle's isothermal law P1V1=P2V2
P1(CH4)=1.45 * 10 ^ 5 Pa
V1(CH4)=2.50 dm^3
V2= 8.00 dm^3
P2(CH4)=(P1(CH4)*V1(CH4))/V2=(1.45 * 10 ^ 5 Pa*2.50 dm^3)/8.00 dm^3= 4.53*10^4 Pa
P1(O2)=2.70 * 10 ^ 5 Pa
V1(O2)= 4.50 dm^3
V2= 8.00 dm^3
P2(O2)=(P1(O2)*V1(O2))/V2= (2.70 * 10 ^ 5 Pa* 4.50 dm^3)/8.00dm^3= 1.52*10^5 Pa
P(tot)= P2(CH4)+P2(O2)=(4.53*10^4 Pa)+(1.52*10^5 Pa)= 1.973*10^5 Pa
b) Now to calculate the molar fractions I need to know the total moles and the moles of the individual gases of the products, but I can't figure out how to get them from the information I have. I know the water vapor temperature is 100 ° C (373.15 F). Could you help me understand how to extrapolate this information? Thank you very much
CH4 (g) + 2O2 (g) -> CO2 (g) + 2H2O (g)
calculate a) the total pressure and partial pressures of the gases before combustion; b) the molar fractions and partial pressures after combustion, knowing that at this temperature the water is in the form of vapor. "
I solved point a) like this:
I apply Boyle's isothermal law P1V1=P2V2
P1(CH4)=1.45 * 10 ^ 5 Pa
V1(CH4)=2.50 dm^3
V2= 8.00 dm^3
P2(CH4)=(P1(CH4)*V1(CH4))/V2=(1.45 * 10 ^ 5 Pa*2.50 dm^3)/8.00 dm^3= 4.53*10^4 Pa
P1(O2)=2.70 * 10 ^ 5 Pa
V1(O2)= 4.50 dm^3
V2= 8.00 dm^3
P2(O2)=(P1(O2)*V1(O2))/V2= (2.70 * 10 ^ 5 Pa* 4.50 dm^3)/8.00dm^3= 1.52*10^5 Pa
P(tot)= P2(CH4)+P2(O2)=(4.53*10^4 Pa)+(1.52*10^5 Pa)= 1.973*10^5 Pa
b) Now to calculate the molar fractions I need to know the total moles and the moles of the individual gases of the products, but I can't figure out how to get them from the information I have. I know the water vapor temperature is 100 ° C (373.15 F). Could you help me understand how to extrapolate this information? Thank you very much