Calculate the volume of 0.16 moles of an ideal gas at 762 mmHg and 26.4 degree C

Question

Calculate the volume of 0.16 moles of an ideal gas at 762 mmHg and 26.4 degree C. b. Calculate the density of CO_2 at 0.99 atm and 1.4 degree C. c. Calculate the volume of a sample of sulfur hexafluoride at middot 74 degree C 1.32 atm if it occupies a volum of 2.8 L at 88.2 degree C and 869 mmHg. d. A 0.988 mol sample of an ideal gas occupies a 10.0 liter flask at 32 degree C and 2.47 atm. If 0.117 mol of the gas are removed from the container, calculate the new pressure. (Assume the temperature remains constant.)

Explanation / Answer

Ideal gas Law:

Pv = nRT

P = Pressure, atm

V = Volume, cm3

R = 82.057 cm3 atm K1 mol1 (gas Constant)

T = Temperature, K

n = number of moles.

Answers:

a) V = ?

n = 0.16

P = 762 mmHg = 1.002632 atm, (Since 1 mmHg = 0.0013157895 atm)

T = 26.4 ° C = 299.55 K (K = ° C + 273)

V = n RT / P = (0.16 mol * 82.057 cm3 atm K1 mol1 * 299.55 K) / 1.002632 atm = 3922.504 cm3

b) Density of CO2 = ?

Let us write down the Ideal gas law again,

Pv = n RT

n = no. of moles = Mass / Molecular weight

P v = (Mass / Molecualr weight) * R * T

We know that, Weight / volume = Density,

So we can re write the equation,

P * Molecular weight = Density * R * T

So, Density = P * MW / ( R * T)

Molecular weight of CO2 = 44 g/mol

Temperature = 1.4 + 273.15 = 274.4 K (Given data)

Density of CO2= 0.99 atm * 44 (g/mol) / (82.057 cm3 atm K1 mol1 * 274.4) = 43.56 / 22516.44

= 0.001934 g/cm3

C) We know one volume, to find the unknown volume, we can relate using Ideal gas law,

(P1 V1 / n R T1) = (P2 V2 / n R T2)

R = Universal constant, so it equals for all the gases.

n = same value for two conditions, since the same sulfur hexafluoride is there in two different conditions,

Given Data:

P1 = 869 mmHg = 1.143421 atm

V1 = 2.8 L = 2800 cm3

T1 = 88.2 ° C = 361.35 K

P2 = 1.32 atm

V2 = ?

T2 = -74 ° C = 199.15 K

Re write the equation to solve for V2 ,

V2 = (T2 / P2) * (P1 V1 / T1) = (199.15 / 1.32) * (1.143421 * 2800 / 361.35) = 637594.42 / 476.98 = 1336.73 cm3

Therefore volume, V2 = 1336.73 cm3 = 1.33673 L

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