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Water is a very weak electrolyte that undergoes the following ionization (called autoionization):$\mathrm{H}_{2} \mathrm{O}(l)$ (a) If $k_{1}=2.4 \times 10^{-5} \mathrm{s}^{-1}$ and $k_{-1}=1.3 \times 10^{11} / M \cdot \mathrm{s}$calculate the equilibrium constant $K$ where $K=$ $\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right] /\left[\mathrm{H}_{2} \mathrm{O}\right] .$ (b) Calculate the product$\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right]$ and $\left[\mathrm{H}^{+}\right]$ and $\left[\mathrm{OH}^{-}\right]$

(a) $K=1.8 \times 10^{-16}$(b) $\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-14}$$\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7}$$\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7}$

Chemistry 102

Chapter 14

Chemical Equilibrium

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10:03

In thermodynamics, a state of thermodynamic equilibrium is a state in which a system is in thermal equilibrium with its surroundings. A system in thermodynamic equilibrium is in thermal equilibrium, mechanical equilibrium, electrical equilibrium, and chemical equilibrium. A system is in equilibrium when it is in thermal equilibrium with its surroundings.

00:54

In chemistry, chemical equilibrium (also known as dynamic equilibrium) is a state of chemical stability in which the concentrations of the chemical substances do not change in the course of time due to their reaction with each other in a closed system. Chemical equilibrium is an example of dynamic equilibrium, a thermodynamic concept.

03:44

Water is a very weak elect…

07:23

04:58

The ionization constant fo…

01:36

to calculate the equilibrium constant for this reaction. Because we know the rate constants in the forward and reverse directions, the equilibrium constant is just going to be a ratio of the rate constant in the forward direction, divided by the rate constant in the reverse direction. So we get a new equilibrium constant of 1.85 times 10 to the negative 16. This rate constant is equal to the concentration of hydrogen ion multiplied by hydroxide divided by the concentration of water. In order to figure out the product of just the hydrogen ion concentration and hydroxide, we need to figure out the concentration of pure water in water. The concentration of pure water in water can be calculated by knowing that if we have a leader of water, we have 100 grams of water. 100 grams of water can be converted into moles of water. Knowing the molar mass of water is 18.1 grams. Then we have moles of water per litre of water 55.5 Moeller. So the equilibrium constant that is equal to this ratio here rearranging, weaken, solve for this product by simply multiplying the equilibrium constant We calculated up here by the water concentration that we calculated here. And we get 1.3 times 10 to the negative 14 because the strike Yama tree of this reaction is one toe one. Then we get one hydrogen ion for everyone hydroxide. So these two concentrations will be equal to each other and they'll both be equal to the square root of the K value or the product of just hydrogen ion multiplied by hydroxide 1.1 10 to the negative seven Moeller.

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