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Can single molecules of C and O2 react in isolation, and if so how will momentum be conserved?

$\ce{C + O2}$ is awfully complicated, so let's just pretend you've asked this: In a single act of the reaction $\ce{H. + H .-> H2}$, how is momentum conserved? That's a legitimate concern all right....
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Why is entropy favorable?

Thermodynamics. The second law of thermodynamics states that entropy always increases in an isolated system. This is taken as a fundamental postulate---we simply accept this statement as a fact ...
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Why would there be a non-zero Gibbs energy of mixing for ideal gases?

When we talk about mixing, we usually mean that two components are in different parts of a container before mixing and then they share the entire container after mixing. In other words, the total ...
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What is the difference between ΔG and ΔrG?

Not for the faint-hearted: There is an excellent, but very mathsy, article here: J. Chem. Educ. 2014, 91, 386 describing the difference. The Gibbs free energy change, $\Delta G$ You are quite right ...
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Why proton concentration is divided by 10⁻⁷?

The textbook is precisely correct. The equilibrium constant $K$ which the logarithm is taken of is dimensionless, and includes activities or fugacities, and not concentrations and pressures. In ...
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Why is entropy favorable?

It appears you're looking for an ELI5-style answer, not an elaborate definition. Entropy just happens – as long as the universe isn't frozen solid, things will always be moving around, and that ...
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If change in free energy (G) is positive, how do those reactions still occur?

$\Delta G^\circ_m$ is the difference in molar Gibbs free energy between the reagents and products in their standard states (in the case of $\ce{AgI(s)}$, the standard state for the reagent is the pure ...
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Why exactly are standard potentials additive?

Following on Derek's great answer, it is very important to remind that the conventional way we use to add half-cell potentials is a consequence of the conservation of energy. Therefore, we should look ...
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True or false: "If a reaction has a large negative value of ∆G, then it will be a fast reaction."

There is the Bell–Evans–Polanyi principle stating that "the difference in activation energy between two reactions of the same family is proportional to the difference of their enthalpy of ...
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Why is entropy favorable?

Do not think of entropy as 'disorder' as this is misleading, better is that it is a 'measure of disorder' but this is equally vague. It is better to think of entropy as the number of ways that '...
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Why would there be a non-zero Gibbs energy of mixing for ideal gases?

With your reply you seem to have answered part of your question. I would like to add a bit about the other part. I will have to do it mathematically first, there is no other shortcut, but then we will ...
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Why can't a reaction go to completion?

You alluded to the answer when you mention activation energy. Kinetically the equilibrium constant is $K_e = k_f/k_b$ where $k_f$ and $k_b$ are the forward are reverse reaction rate constants in the ...
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Pressure at which graphite and diamond are in equilibrium

For each phase $i$ (graphite or diamond) you can show that $$\mathrm{d}\mu _i = V_i \mathrm{d}p - S_i \mathrm{d}T$$ or after integration $$\mu_i = \mu_i^\circ+\int_{p^\circ}^{p} V_{i} dp$$ at ...
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Gibbs Free Energy Notation

$G$ is the Gibbs free energy of a system. It is a conceptual quantity in the sense that there is no reference point that defines $G = 0$ for a substance (unlike entropy). Whenever you see a plot of $G$...
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How to estimate the temperature needed to overcome an activation energy barrier?

You could convert the rate constant($k$) to half-life($t_{1/2}$) which would give you an idea of the time scale required for the reaction to finish at a certain temperature. The equation to obtain ...
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How to estimate the temperature needed to overcome an activation energy barrier?

From the Eyring equation, we can simply calculate the $k$ value for it. \begin{align} k &= \frac{k_\mathrm{b} T}{h}\exp\left(\frac{-\Delta G^\ddagger}{RT}\right)\\ k_\mathrm{b} &= \pu{1.38E-9 ...
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How can a nonspontaneous reaction occur?

When you add energy from somewhere, let's say a battery, you are creating a greater amount of entropy there (in the battery or whatever). That's all there is to it. The Second Law is not violated. The ...
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Why is my conclusion inconsistent with the van't Hoff equation?

In the linear form $y = mx + b$, both $m$ and $b$ are constants, i.e. they don't depend on $x$. On the other hand, $\Delta G^\circ$ definitely depends on the temperature (and consequently on its ...
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How to explain disagreement between Le Châtelier's principle and the simplified Gibbs free energy equation?

The primary flaw in your reasoning is assuming that $K$ is proportional to $-\Delta G^\circ$, so that a reaction with $\Delta S^\circ >0$ and $\Delta G^\circ<0$ must have a larger $K$ at a ...
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Are all exothermic reactions spontaneous?

No, it is not the case that all exothermic reactions are spontaneous. More generally, it doesn't even make sense to make a broad statement that a reaction is or is not spontaneous without also ...
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Here is a function that works: https://www.desmos.com/calculator/cqwgfj2nzt The general function would be $$a \left( \frac{b}{1 - e^{5-x}} - \frac{c}{1 - e^{10-x}} \right)$$ I'm sure you could ...