Nickel tetracarbonyl, a volatile liquid used to purify...

Nickel tetracarbonyl, a volatile liquid used to purify nickel, forms when carbon monoxide contacts nickel. For $\operatorname{Ni}(\mathrm{CO})_{4}(l), \quad \Delta H_{\mathrm{f}}^{\circ}=-633.0 \mathrm{kJ} / \mathrm{mol}$ and $S^{\circ}=313.4$ $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ $$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(l)$$ (a) Calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for the reaction under standard-state conditions at $25^{\circ} \mathrm{C}$ . (b) Estimate the temperature at which the reaction becomes nonspontaneous. (c) Calculate $\Delta G_{\mathrm{f}}^{\circ}$ for $\mathrm{Ni}(\mathrm{CO})_{4}(l)$ .

Nickel tetracarbonyl, a volatile liquid used to purify nickel, forms when carbon monoxide contacts nickel. For $\operatorname{Ni}(\mathrm{CO})_{4}(l), \quad \Delta H_{\mathrm{f}}^{\circ}=-633.0 \mathrm{kJ} / \mathrm{mol}$ and $S^{\circ}=313.4$ $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$
$$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(l)$$
(a) Calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for the reaction under standard-state conditions at $25^{\circ} \mathrm{C}$ .
(b) Estimate the temperature at which the reaction becomes nonspontaneous.
(c) Calculate $\Delta G_{\mathrm{f}}^{\circ}$ for $\mathrm{Ni}(\mathrm{CO})_{4}(l)$ .

Key Concepts

Standard Thermodynamic Quantities

Standard thermodynamic quantities such as enthalpy (?H°), entropy (S°), and Gibbs free energy (?G°) are fundamental state functions used to describe the energy and disorder of a system under defined conditions. They enable the prediction of reaction favorability and provide a quantitative measure of the energy changes when chemical species form or react.

Gibbs Free Energy Equation

The Gibbs free energy equation, ?G = ?H - T?S, is central in chemical thermodynamics. It combines enthalpic and entropic contributions to determine reaction spontaneity. This relationship indicates that a reaction is spontaneous when ?G is negative. The balance between ?H and T?S explains how temperature impacts the reaction's driving force.

Reaction Spontaneity

Reaction spontaneity refers to whether a process will proceed without external input, which is predicted by the sign of ?G. Negative ?G indicates a spontaneous reaction under the given conditions. This concept helps in assessing whether a reaction will occur and is influenced by both the enthalpy and entropy changes of the system.

Temperature Dependence of Spontaneity

Temperature plays a critical role in determining reaction spontaneity through its effect on the T?S term in the Gibbs free energy equation. By setting ?G equal to zero, one can estimate the temperature at which a reaction transitions from spontaneous to nonspontaneous. This approach highlights the interplay between energy change (?H) and disorder (?S) in dictating reaction behavior.

Free Energy of Formation

The free energy of formation (?Gf°) of a compound is defined as the change in free energy when one mole of the compound is formed from its elements in their standard states. It is a crucial quantity in thermodynamics, as it provides a benchmark for comparing the relative stability of different substances and predicting the direction of chemical reactions.

Transcript

00:01 We calculate several thermodynamic properties of the synthesis of nickel tetrocarbonil.

00:07 So the first thing we're going to do is calculate our enthalpy of reaction.

00:13 So to do this, we are going to subtract our reactants from our products using our standard enthalpyes of formation.

00:20 So starting with our products for our nickel tetracharboneal, we are given in the problem a delta h of formation of negative 633 .3 .3.

00:31 0 .0 kilojoules per mole.

00:35 For our reactants here we have that our nickel solid is going to be 0 kilojoules per mole because of solid metal.

00:42 And we're going to add that to 4 times our carbon monoxide, which is going to be negative 100 .5 kilojoules per mole.

00:53 This gives us a delta h standard value of negative 191 kilojoules per mole.

01:03 So we're going to calculate our delta s value in a very similar way.

01:07 We're going to use our standard delta s for each of these molecules, products minus reactants.

01:12 So we're given the problem that our standard delta s for nickel tetracharboneal is 313 .4 joules per mil kelvin.

01:24 Subtract that from our reactants here, where we have for nickel 29 .9 jules per mole kelvin plus our four times our carbon monoxide, which is going to be 197 .6 joules per mole kelvin.

01:42 This gives us a delta s standard value of negative 503, excuse me, 506 .9 joules per mole kelvin, or negative 0 .5069 kilojoules per mole.

02:02 So now that we have both of these values, we can go ahead and calculate our delta g.

02:07 We're going to use the equation here that our delta g standard is equal to our delta h standard minus t.

02:13 D -delta -s standard.

02:16 So we can go out and plug in some numbers here.

02:18 We know that negative 191 kilojoules per mole.

02:24 We're running at a temperature of 298 kelvin, so we can do that for our standard temperature, and then our entropy is going to be 0 .5069 kilojoules per mole kelvin.

02:40 This is going to give us a delta g standard value of negative 39 .9 kilojoules per mole.

02:56 Okay, so now that we have this value, we can do a couple different things.

03:01 First, we're going to calculate the temperature at which this reaction becomes non -spontaneous...

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