Answer to Question #100221 in General Chemistry for Beverlie

Question

1.You have a cylinder of argon gas at 19.8 atm of pressure at 19 oC. The volume of the cylinder is 50.0 L. What would be the volume of the gas if you were to decrease the pressure to 0.974 atm? Assume constant temperature.
2. Helium gas at 22 oC and 1.00 atm occupies a vessel has a volume of 2.54 L. What would be the volume if the gases temperature was decreased to -197 oC? Assume constant pressure
3. A cylinder contains 91.3 g of oxygen gas. If the volume of the cylinder is 8.58 L, what is the pressure of the gas in atmospheres if gas temperature is 21 oC? Calculate the pressure using the ideal gas equation and the van der Waals equation.
4. Calculate the density of H2S gas at 56 oC and 967 mmHg. Obtain the density in grams per liter.

Answer 1

nRT=PV (Mendeleev-Klapeyrones"s law : ideal gas equation), n - number of moles, R - gase constant 8.314 J/K*mole = 0.0821 l *atm/mol * K , T - absolutly temperature K,

P - pressure, - V - volume ; D - density

(4) 1 moles H₂S weight: 34 g;

T(C)+273,15=T(K)

V=nRT/P

V=1 * 0.0821 (l *atm/mol * K ) * 329,15 * K / (967/760 atm)

V = 21,2385 l =21,24 l

D = Weight / volume

D = 34 g / 21,24 l = 1,600 g/l=1,6 g/l

(2) P = const = 1 atm

T₁ =295,13K

V₁=2,54 l

T₂=76,15K

nRT=PV

nR/P = V / T => n =const, R= const, P = const, V/T = const => V₁/T₁ =V₂/T₂

V₂=V₁*T₂/T₁

V₂=0,65537=0,655 l

(1)

nRT=PV, n - const, R -const, T -const, PV -const => P₁V₁=P₂V₂

P₁=19,8 atm

V₁=50 l

P₂=0,974 atm

V₂=?

V₂=P₁V₁/P₂ => 19,8atm*50 l/0,974atm = 1016,4 l

(3) n(O2)=weight/MolarWeight = 91,3g/32g=2,85 mole, R - 0.0821 l*atm/mole*k

V=8,58 l

P=?

T(K)=294,15

nRT=PV

P=nRT/V

P=8,021 atm

Van-Der-Vaals equation:

(p + n² *a²/V²)(V-n*b)=nRT

As a first approximation, we take the volume V=V₁ obtained from the ideal gas equation

V₁=nRT/P

V₁=V

V₁=8,58L

P1=8,021 atm

P_i=n² *a²/V²₁

P_i=0,015 atm

second approximation

V₂=nRT/(p+p_i)+nb

V₂=8,5808+0,09006=8,67L

V₂=nRT/P

V₂=2,85*0,0821*294,15/P

P=7,94

p_i2=n²*a²/V²₂

p_i2=0,00199

third(?)

V3=nRT/(p+p_i2) +nb=8,7L

P=7,92

Further deviations in approximations of insignificant