The ideal gas law describes the relationship among the volume of an ideal gas (V

Question

The ideal gas law describes the relationship among the volume of an ideal gas (V), its pressure (P), its absolute temperature (T), and number of moles (n): PV = nRT Under standard conditions, the ideal gas law does a good job of approximating these properties for any gas. However the ideal gas law does not account for all the properties of real gases such as intermolecular attraction and molecular volume, which become more pronounced at low temperatures and high pressures. The van der Waals equation corrects for these factors with the constants a and b, which are unique to each substance: (P + an^2/V^2)(v -nb)= nRT The gas constant R is equal to 0.08206 L . atm/(K . mol). A3.00-L flask is filled with gaseous ammonia, NH_3. The gas pressure measured at 15.0^degree C is 1.35 atm . Assuming ideal gas behavior, how many grams of ammonia are in the flask Express your answer to three significant figures and include the appropriate units. In the following part you can see how the behavior of real gases deviates from the ideal behavior. You will calculate the pressure values for a gas using the ideal gas law and also the van der Waals equation. Take note of how they differ. If 1.00 mol of argon is placed in a 0.500-L container at 25.0^degree C , what is the difference between the ideal pressure (as predicted by the ideal gas law) and the real pressure (as predicted by the van der Waals equation) For argon, a = 1.345 (L^2 . atm)/mol^2 and b = 0.03219 L/mol. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Part A

Using ideal gas law equation

PV = nRT

(1.35)(3) = n * 0.0821 * (273+15)

n = 4.05/(0.0821 * 288) = 0.1713 moles

Molar mass of NH3 (ammonia) = 14 + 3 * 1 = 17 gm/mol

Mass of NH3 in flask = number of moles * molar mass

=> 0.1713 * 17 = 2.912 gms

Part B

Using the ideal gas law

PV = nRT

P(0.500) = 1 * 0.0821 * (273+25)

P = 2 * 0.0821 * 298 = 48.9316 atm

Using the vanderwalls equation

(P + 1.345/(0.5)^2 ) (0.5 - 0.03219) = 1 * 0.0821 * 298

(P + 1.345/(0.5)^2 ) (0.5 - 0.03219) = 24.4658

(P + 5.38) = 52.298

P = 46.918 atm

Pideal - Preal = 48.9316 - 46.918 = 2.0136 atm

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