An analytical laboratory ships high-purity ammonia gas (NH ) to field stations in…

CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures

Problem

An analytical laboratory ships high-purity ammonia gas (NH

_3

) to field stations in portable cylinders. During transit, interior temperatures may reach

328\,\text{K}

, and regulations limit the maximum cylinder pressure to

5.00\,\text{atm}

. To ensure accurate flow-rate measurements made with the ideal-gas equation, the laboratory requires the compressibility factor of the contained NH

_3

to remain within

\pm2.0\%

of unity under all anticipated conditions. For ammonia, the van der Waals parameters are

a=4.17\,\text{L}^2\,\text{atm}\,\text{mol}^{-2}

and

b=0.0371\,\text{L}\,\text{mol}^{-1}

. (a) Calculate the compressibility factor

Z

for NH

_3

T=298\,\text{K}

and

P=5.00\,\text{atm}

. Show your calculations clearly. (b) Repeat the calculation for the worst-case transit condition of

T=328\,\text{K}

and

P=5.00\,\text{atm}

. State whether the deviation criterion is still met. (c) If the criterion is not satisfied at

328\,\text{K}

, determine the maximum allowable pressure at that temperature that will bring

Z

back within

\pm2.0\%

. Express your answer to three significant figures. (d) Draft a brief operational guideline for cylinder filling that specifies the maximum permissible fill pressure at room temperature (

298\,\text{K}

) to guarantee compliance throughout shipping. Support your recommendation with quantitative evidence and discuss any practical considerations such as safety margins.

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