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Imagine you are doing a process which takes 'n' steps. Label the steps : 1,2,3..n, now consider the time it takes to do step 1 , step -2 and so on. Now, wouldn't you agree that the time taken to complete process would be entirely dependent on the step which takes the most time(slowest step) to complete? So, in your example the hydrogen ions are in one of the ...

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As a purely mathematical definition, a first order reaction is one in which the rate is directly proportional to concentration of reactants. The thing you should look for is physical examples of this. This only happens if you have reactions where one compound is decreasing and the other one is abundance (pseudo - first order) , or , radioactive decay where ...

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First order reactions are always about the total count or particles, molar amount or mass. $$\frac {\mathrm{d}n}{\mathrm{d}t} = -k \cdot n$$ $$\frac {\mathrm{d}m}{\mathrm{d}t} = -k \cdot m$$ The point of using concentration instead is, that it is proportional to them in homogenous, constant volume scenario. $$c = \frac nV$$ $$c = \frac m{MV}$$ so it can be ...

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For first order reactions (assuming the reaction $\ce{A -> B + C}$): $$-\frac{\mathrm{d}[\ce{A}]}{\mathrm{d}t} = k[\ce{A}]$$ If the volume is $V(t)$, then $[\ce{A}] = \frac{n}{V(t)}$. You will have to substitute $[\ce{A}]$ in the differential equation and solve it in order to obtain the rate equation in this case. As for finding the half-life, Wikipedia ...

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This question has more physics into it than chemistry but the ice melting to provide a slippery surface (and guess subsequently re-freeze) makes sense. We can also try asking someone to glide over dry-ice made out of carbon-dioxide instead of regular ice and see if there is any increase or decrease in the friction . Two possibilities - (a) If water ...

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There's a very nice—and fairly accessible—discussion of your third question in Nature Magazine's News and Views Section[1]. In this article, Bonn discusses the results of a fairly recent work that appeared in Physical Review X[2]. Bonn summarizes the key points as follows: The idea that a thin film of meltwater wets the surface of ice has been accepted ...

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Calderon & Mohazzabi give an excellent summation of the various theories proposed through the years to explain why ice is so slippery in their 2018 paper "Premelting, Pressure Melting, and Regelation of ice revisited" in the Journal of Applied Mathematics and Physics. They offer both theoretical and experimental evidence that neither pressure ...

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Suppose you have a sample of $\ce{N}$ atoms of a radioactive material. As it is radioactive, you may state that a small fraction k is decomposed by second. This fraction does not depend on the total number of atoms. If this sample is placed in a Geiger counter, each decomposition of its atoms produces a ray that crosses the inner volume of the Geiger counter,...

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I found the answer. First, we need to find balanced equation for reaction. Then express the concentration of $xˆst$ in the steady state through E. Then we can arrive to this kind of solution for the value of E. $\displaystyle{E\frac{x_0 - \frac{x_o}{2}}{K + x_0 - \frac{x_0}{2}}} - {\frac{\frac{x_0}{2}}{K + \frac{x_0}{2}}} = 0.$ \$\displaystyle{E\frac{\frac{...

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Isotopes differ in mass. Otherwise the same molecules but with the different mass have the different mean speed. The different speed means the different molecular collision rate. The different collision rate means the different kinetic constants. There are some indirect effects of different isotop mass on the kinetics, but these are much smaller than the ...

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