Large amounts of nitrogen gas are used in the manufacture of a...

Question

Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 120.00 kg of N₂(g) is stored in a 1100.0-L metal cylinder at 280 °C. (c) Under the conditions of this problem, which correction dominates, the one for finite volume of gas molecules or the one for attractive interactions?

Accepted Answer

First, understand the context of the problem. We are dealing with real gases, which deviate from ideal behavior due to finite volume of gas molecules and attractive interactions between them. The Van der Waals equation accounts for these deviations.. The Van der Waals equation is given by:

(P + \frac{a n^{2}}{V^{2}}) (V - nb) = nRT

, where

P

is pressure,

V

is volume,

n

is moles,

R

is the gas constant,

T

is temperature, and

a

and

b

are Van der Waals constants specific to the gas.. Calculate the number of moles of nitrogen gas using the formula:

n = \frac{mass}{molar mass}

. The molar mass of nitrogen gas

N_{2}

is approximately 28.02 g/mol.. Determine the significance of the Van der Waals constants

a

and

b

for nitrogen. The constant

a

accounts for attractive forces, while

b

accounts for the finite volume of molecules.. Compare the magnitude of the corrections. If the correction term involving

a

is larger, attractive interactions dominate. If the correction term involving

b

is larger, the finite volume of gas molecules dominates. This can be assessed by calculating the terms

\frac{a n^{2}}{V^{2}}

and

nb

.

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Key Concepts

Ideal Gas Law

Real Gas Behavior

Van der Waals Equation