Calculation Of Partial Pressures And Total Pressure Of A Gas Mixture

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Calculation Of Partial Pressures And Total Pressure Of A Gas Mixture

Given that volume = V liters; pressure = P atmosphere; temperature = T Kelvin; Numuber of Moles = n.
**Boyle's Law: V α 1/P (constant n, T)**
**Charle's Law: V α T (constant n, P)**
**Avogadro's Law: V α n (constant P, T)**
**Ideal Gas Equation: V α nT/P ; V = nRT/P (R is proportionality constant = 0.0821 L-atm/mol-K**)
**Dalton's Law: P _{t} = Σ_{i = 1-n} P_{i} = P_{1} + P_{2} ... P_{n}**.

Where P

Where n

(a) Consider the following gas mixing apparatus:

(i) What is the partial pressure of N

(ii) What is the partial pressure of O

(b) A mixture containing 0.538 mol of He(g), 0.315 mol of Ne(g), and 0.103 mol Ar(g) is confined in a 7 L vessel at 25

(i) Calculate the partial pressures of each of the gases in the mixture

(ii) Calculate the total pressure of the mixture.

(c) A piece of solid carbon dioxide with a mass of 5.50 g is placed in a 10 L vessel that already contain air at 705 torr and 24

(d) A mixture of gases contains 0.75 mol N

(e) At an underwater depth of 250 ft, the pressure is 8.38 atm. What should the mole percent of oxygen be in the diving gas for the partial pressure of oxygen in the mixture to be 0.21 atm, the same as in air at 1 atm.

(f) A quantity of N

**The strings**:
S_{7}P_{3}A_{32} (force - push).
**The math**:

Pj Problem of Interest is of type *force* (push).
**(a)** n = PV/RT calculates the initial moles of N_{2} and O_{2} in the apparatus:

So, n_{N2} = 1x2/(0.0821x298) = 2/24.465 = 0.082 mol of N_{2}

So, n_{O2} = 2x3/(0.0821x298) = 6/24.465 = 0.245 mol of O_{2}

P = nRT/V (note new volume of gases = 5 L)

So, P_{N2} = (0.082x0.0821x298)/5 = 0.40 atm

So, P_{O2} = (0.245x0.0821x298)/5 = 1.20 atm

So, P_{t = PN2 + PO2 = 0.40 + 1.20 = 1.60 atm.
(b) P = nRT/V
So, PHe(g) = (0.538x0.0821x298)/7 = 1.88 atm
So, PNe(g) = (0.315x0.0821x298)/7 = 1.10 atm
So, PAr(g) = (0.103x0.0821x298)/7 = 0.360 atm
So, Pt = 1.88 + 1.10 + 0.360 = 3.34 atm.
(c) P = nRT/V
Molar mass of CO2 = 44 g
So, mol of 5.5 g = 5.5/44 = 0.125 mol
So, PCO2 = 0.125x0.0821x297)/10 = 0.305 atm
Pair = 705/760 atm = 0.928 atm
So, Pt = 0.305 + 0.928 = 1.233 atm.
(d) Pi = (ni/nt)Pt.
nt = 0.75 + 0.30 + 0.15 = 1.20 mol
Pt = 1.56 atm
So, PN2 = (0.75/1.20)1.56 = 0.975 atm
So, PO2 = (0.30/1.20)1.56 = 0.39 atm
So, PCO2 = (0.15/1.20)1.56 = 0.195 atm.
(e) Pi = (ni/nt)Pt
Mole percent = (ni/nt)100
PO2 = 0.21 atm
Pt = 8.38 atm
Pi = (ni/nt)Pt
So,(ni/nt)100 = (0.21/8.38)100 = 2.5%.
(f) n = PV/RT
So, original nN2 = (1x4.75)/(0.0821x299) = 4.75/24.548 = 0.1935 mol
So, original nO2 = (5.25x5)/(0.0821x299) = 26.25/24.548 = 1.069 mols
After transfer to 10 L container:
PN2 = nRT/V = (0.1935x0.0821x293)/10 = 0.466 atm
PO2 = nRT/V = (1.069x0.0821x293)/10 = 2.572 atm
So, Pt = 0.466 + 2.572 = 3.038 atm.
}

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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