In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at \(43^{\circ} \mathrm{C}\) : $$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g)$$ This reaction separates nickel from other solid impurities. (a) Starting with \(86.4 \mathrm{~g}\) of \(\mathrm{Ni}\), calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume \(4.00 \mathrm{~L}\). (Assume the above reaction goes to completion.) (b) On further heating the sample above \(43^{\circ} \mathrm{C}\), it is observed that the pressure of the gas increases much more rapidly than predicted based on the ideal gas equation. Explain.

Step by step solution

01

Reactant to Product Conversion

Calculate the number of moles \(n\) of Ni used in the reaction using its molar mass. As \(n = \frac{mass}{molar~mass}\), and the molar mass of Ni is approximately \(58.69 \mathrm{g/mol}\), so \(n = \frac{86.4g}{58.69g/mol} = 1.47 mol\). In the reaction, 1 mol of Ni forms 1 mol of Ni(CO)₄. Hence, \(1.47 mol\) of Ni forms \(1.47 mol\) of Ni(CO)₄.

02

Calculate Pressure of Ni(CO)₄

The pressure \(P\) of the Ni(CO)₄ can be calculated using the ideal gas equation \(PV=nRT\), where \(R = 0.0821 L·atm/mol·K\) and temperature \(T = 43^{\circ} \mathrm{C} = 273 + 43 = 316K\). Rearranging for \(P\), we get \(P = \frac{nRT}{V}\) = \(\frac{1.47 * 0.0821 * 316}{4.00}\) ≈ 9.57 atm.

03

Explain Deviation

At temperatures above \(43^{\circ} \mathrm{C}\), pressure increases rapidly due to the breakdown of tetracarbonylnickel into nickel and carbon monoxide, thus increasing the number of gas molecules beyond what is expected for an ideal gas behaving according to \(PV=nRT\). Additionally, at higher pressures, the gases no longer behave ideally due to factors such as intermolecular interactions and the non-zero volumes of gas particles.

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