how to calculate partial pressures?
A mixture containing 2.53 g each of CH4(g), C2H4(g) and C4H10(g) is contained in a 1.50 L flask at a temperature of 25°C.
(a) Calculate the partial pressure of each of the gases in the mixture.
(b) Calculate the total pressure of the mixture.
Answers in atmospheres.
how do I do this and what are the answers?
stevo
Comments
The total pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases.
A partial pressure is the pressure that a gas in a mixture would exert if it were the only gas present under the same conditions.
There are two ways to solve this problem.
(1) First to find the partial pressures and then the total pressure as it is stated in your question. (Long way)
(2) First to find the total pressure and then the partial pressures. (Short way)
(1) First, the number of moles of each gas is calculated:
CH4 = 2.53 g / 16 g/ mol = 0.158 mol
C2H4 = 2.53 g / 28 g/ mol = 0.090 mol
C4H10 = 2.53 g / 58 g/ mol = 0.044 mol
Second, the pressure of each gas is calculated by using ideal gas law.
V = 1.50 L
T = 25°C = 298 K
R = 0.082 atm.L/mol.K
P = nRT/V
CH4 => P = (0.158)(0.082)(298) / (1.5) = 2.57 atm
C2H4 => P = (0.090)(0.082)(298) / (1.5) = 1.46 atm
C4H10 => P = (0.044)(0.082)(298) / (1.5) = 0.72 atm
Pt = 2.57 + 1.46 + 0.72 = 4.75 atm
(2) First find the total pressure:
Pt = ntRT/V
nt = 0.158 + 0.090 + 0.044 = 0.292 mol
Pt = (0.292)(0.082)(298) / (1.5) = 4.75 atm
Since the partial pressures of gases are directly proportional to their number of moles;
P(CH4) / Pt = n(CH4) / nt
P(CH4) = pt x [n(CH4) / nt]
P(CH4) = 4.75 x [0.158 / 0.292] = 2.57 atm
P(C2H4) = 4.75 x [0.090 / 0.292] = 1.46 atm
P(C4H10) = 4.75 x [0.044 / 0.292] = 0.72 atm
or the last one can be found by the difference;
P(C4H10) = 4.75 - (2.57 + 1.46) = 0.72 atm
How To Calculate Partial Pressure
Partial Pressure Formula
Because it is dependent solely the number of particles and not the identity of the gas, the Ideal Gas Equation applies just as well to mixtures of gases is does to pure gases. In fact, it was with a gas mixture—ordinary air—that Boyle, Gay-Lussac, and Charles performed their early experiments. The only new concept we need to deal with gas mixtures is partial pressure, a concept invented by the famous English chemist John Dalton (1766-1844). Dalton correctly reasoned that the low density and high compressibility of gases were indicative of the fact that they consisted mostly of empty space; from this, it Dalton concluded that when two or more different gases occupy the same volume, they behave entirely independently of one another.
Dalton's Law (also called Dalton's Law of Partial Pressures) states that the total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases. Mathematically, this can be stated as follows:
where P1, P2 and Pn represent the partial pressures of each compound. It is assumed that the gases do not react with each other.
The partial pressure of one individual gas within the overall mixtures, pi, can be expressed as follows:
where xi is the mole fraction.
Example
A mixture of 2 mol H2 and 3 mol He exerts a total pressure of 3 atm. What is the partial pressure of He?
- shoptexaselectricity
If you assume that you have ideal gases, then
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant (8.3145 J/(Kmol) or 0.08206 Latm/(K mol) ), and T is an absolute temperature (such as Kelvin). You are given the volume and the temperature, so the only variables are n and P.
First use the atomic weights to convert each mass of each chemical to a number of moles of each chemical. This gives you n values, so that you can compute P values.
The total pressure is found when you use the total number of moles (add the n's together). If you only use the number of moles of one chemical, such as CH4 gas, you will get a smaller pressure. This pressure is the partial pressure of CH4, its additive contribution to the total pressure.
Good luck computing the answers.
What if we aren't givin a temperature or moles? such as, A 285-mL flask contains pure helium at a pressure of 757torr . A second flask with a volume of 495mL contains pure argon at a pressure of 715torr.
If the two flasks are connected through a stopcock and the stopcock is opened, what is the partial pressure of helium? PHe=______torr