Answer to Question #109619 in General Chemistry for Jonathan

Question

A 27g sample of NH3 (Ammonia) gas has a volume of 1.73 L at a temperature of 63°C.
i. Calculate the pressure using the Ideal Gas Law.
ii. Calculate the corrected pressure using the Van der Waals Equation.
atm×L2 L a=4.166 mol2 b=0.03713 mol

Answer 1

Solution:

T = 63°C = 336.15 K

V = 1.73 L

R = 0.08206 L atm mol^-1 K^-1

Part "i":

The Ideal Gas Law can be written as: PV = nRT,

where P, V and T are the pressure, volume and temperature; n is the amount of substance; and R is the ideal gas constant.

Let's calculate the amount of NH₃:

Mr(NH₃) = 17.031 g/mol.

Moles of NH₃ = n(NH₃) = m(NH₃) / M(NH₃) = (27 g) / (17.031 g/mol) = 1.5853 moles.

Let's calculate the pressure using the Ideal Gas Law:

PV = nRT

(P * 1.73 L) = (1.5853 mol * 0.08206 L atm mol^-1 K^-1 * 336.15 K)

P = (1.5853 mol * 0.08206 L atm mol^-1 K^-1 * 336.15 K) / (1.73 L) = 25.28 atm

P_i = 25.28 atm.

Part "ii":

The Van der Waals Equation can be written as: [P + an²/V²] * [V - nb] = nRT,

where a and b - specific constants for NH₃

a = 4.166 L² atm mol^-2

b = 0.03713 L mol^-1

Let's calculate the pressure using the Van der Waals Equation:

[P + an²/V²] * [V - nb] = nRT

[P + 4.166*1.5853² / 1.73² ] * [1.73 - 1.5853*0.03713] = 1.5853 * 0.08206 * 336.15

[P + 3.4982] * 1.6711 = 43.7297

P + 3.4982 = 26.1682;

P_ii = 22.67 atm.

Answer:

P_i = 25.28 atm;

P_ii = 22.67 atm.