Question

Calculate $\left[{\mathrm{OH}}^{-}\right]$ in a $3.0\times {10}^{-7}-$ M solution of $\mathrm{Ca}(\mathrm{OH}{)}_2$

Short answer

The concentration of ${\mathrm{OH}}^{-}$ ions in the $3.0\times {10}^{-7}\mathrm{M}$ solution of $\mathrm{Ca}(\mathrm{OH}{)}_2$ is 6.0 x ${10}^{-7}\mathrm{M}$.

Step-by-step solution

Write the balanced chemical equation for the reaction

The dissociation of $\mathrm{Ca}(\mathrm{OH}{)}_2$ in water can be represented by the following equation: $$\mathrm{Ca}(\mathrm{OH}{)}_2\to {\mathrm{Ca}}^{2+}+2{\mathrm{OH}}^{-}$$ This equation tells us that for each mole of $\mathrm{Ca}(\mathrm{OH}{)}_2$ that dissociates, two moles of ${\mathrm{OH}}^{-}$ ions are produced.

Calculate the moles of ${\mathrm{OH}}^{-}$ produced

From the stoichiometry of the reaction, we know that 1 mole of $\mathrm{Ca}(\mathrm{OH}{)}_2$ will produce 2 moles of ${\mathrm{OH}}^{-}$. Given the concentration of $\mathrm{Ca}(\mathrm{OH}{)}_2$, we can find out the amount of ${\mathrm{OH}}^{-}$ produced: The concentration of $\mathrm{Ca}(\mathrm{OH}{)}_2$, 3.0 x ${10}^{-7}\mathrm{M}$. To find the concentration of ${\mathrm{OH}}^{-}$, we multiply the concentration of $\mathrm{Ca}(\mathrm{OH}{)}_2$ by 2, as per the balanced equation: $$[{\mathrm{OH}}^{-}]=2\times [\mathrm{Ca}(\mathrm{OH}{)}_2]$$

Calculate the concentration of ${\mathrm{OH}}^{-}$

By plugging in the given concentration of $\mathrm{Ca}(\mathrm{OH}{)}_2$, we can calculate the concentration of ${\mathrm{OH}}^{-}$ ions: $$[{\mathrm{OH}}^{-}]=2\times (3.0\times {10}^{-7}\mathrm{M})$$ $$[{\mathrm{OH}}^{-}]=6.0\times {10}^{-7}\mathrm{M}$$ The concentration of ${\mathrm{OH}}^{-}$ ions in the solution is 6.0 x ${10}^{-7}\mathrm{M}$.

Key concepts

Chemical Equilibrium

Chemical equilibrium refers to the state in a chemical reaction where the concentrations of reactants and products remain constant over time. In a reaction at equilibrium, the forward reaction rate equals the reverse reaction rate. This balance does not mean the concentrations are equal, but rather that their proportions don't change over time.
In the context of dissociation reactions like in the problem with calcium hydroxide ( Ca( OH)_2), understanding equilibrium can help predict how the reaction will shift when concentrations change. Even though Ca( OH)_2 is dissociating and not reaching a classical equilibrium like reversible reactions do, it's important to note the concept of saturation which can influence dissociation.
In saturated solutions or when conditions change, the dissociation could potentially reach a dynamic equilibrium. Understanding these principles is vital for predicting behavior in more complex chemical equilibria.

Stoichiometry

Stoichiometry helps chemists to calculate the relationships between reactants and products in a chemical reaction. It involves the use of balanced chemical equations to figure out the proportions needed or produced of various substances.
In the dissociation reaction of Ca( OH)_2, stoichiometry revealed that two moles of OH^- are produced for every mole of Ca( OH)_2. This 2:1 ratio is crucial for accurate calculations. With the given molarity of Ca( OH)_2, multiplying it by the stoichiometric coefficient gives us the molarity of the hydroxide ion ( OH^-).
Stoichiometry isn't just about balancing equations; it's a tool to translate chemical symbols into measurable quantities that can be compared and used practically in labs and industries. It's all about using ratios smartly to link the microscopic world of atoms to the macroscopic world we can measure.

Molarity

Molarity, or molar concentration, is a measure of concentration representing the moles of a solute per liter of solution. It is essential for various calculations in chemistry, as it provides a way to quantify the concentration of substances in a solution.
In the given problem, the molarity of Ca( OH)_2 is used to calculate the resulting concentration of OH^- ions after dissociation. Knowing the initial molarity of a reactant helps predict how much of a product will form, especially in reactions involving dissociation or chemical equilibrium.
Understanding molarity allows chemists and students alike to work with solutions accurately, whether it's preparing them in the laboratory or predicting the yield of a given reaction. It serves as the foundation for communicating concentrations in a standard and universally understood format.

Dissociation Reaction

Dissociation reactions involve the separation of a compound into ions when dissolved in water. In the case of Ca( OH)_2, it dissociates to form Ca^{2+} and 2 OH^- ions. This type of reaction is essential in understanding the behavior of ionic compounds in solutions.
When a compound like Ca( OH)_2 is added to water, it breaks down into its constituent ions, showing the ionic nature of the compound. This dissociation is key to understanding how such compounds contribute to the solution's characteristics, like pH or electrical conductivity. For Ca( OH)_2, the generation of OH^- ions increases the solution's basicity.
Grasping the concept of dissociation is crucial in chemistry for predicting how substances interact in aqueous solutions. It's the driving force behind processes ranging from acid-base reactions to the solubility of salts, shaping our understanding of chemical behavior in water-based systems.