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Ignoring protolysis reactions, indicate the concentration of each ion or molecule present in the following solu- tions: (a) \(0.35 \mathrm{MK}_{3} \mathrm{PO}_{4},\) (b) \(5 \times 10^{-4} \mathrm{MCuCl}_{2},(\mathbf{c}) 0.0184\) \(\mathrm{MCH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathbf{d})\) a mixture of \(35.0 \mathrm{~mL}\) of \(0.010 \mathrm{MNa}_{2} \mathrm{CO}_{3}\) and \(50.0 \mathrm{~mL}\) of \(0.200 \mathrm{MK}_{2} \mathrm{SO}_{4}\). Assume the volumes are additive.

Short Answer

Expert verified
For the given solutions: (a) $0.35 \mathrm{MK}_{3} \mathrm{PO}_{4}$: We have $[K^+] = 1.05 \mathrm{M}$ and $[PO_{4}^{3-}] = 0.35 \mathrm{M}$. (b) \(5 \times 10^{-4} \mathrm{MCuCl}_{2}\): We have $[Cu^{2+}] = 5 \times 10^{-4} \mathrm{M}$ and $[Cl^-] = 1 \times 10^{-3} \mathrm{M}$. (c) $0.0184 \mathrm{MCH}_{3} \mathrm{CH}_{2} \mathrm{OH}$: No ions are formed, and the concentration of CH鈧僀H鈧侽H is $0.0184 \mathrm{M}$. (d) Mixture of $35.0 \mathrm{~mL}$ of $0.010 \mathrm{MNa}_{2} \mathrm{CO}_{3}$ and $50.0 \mathrm{~mL}$ of $0.200 \mathrm{MK}_{2} \mathrm{SO}_{4}$: We have $[Na^+] = 0.0082 \mathrm{M}$, $[CO_{3}^{2-}] = 0.0041 \mathrm{M}$, $[K^+] = 0.236 \mathrm{M}$, and $[SO_{4}^{2-}] = 0.118 \mathrm{M}$.

Step by step solution

01

(a) Determine ion concentrations in 0.35 M K鈧働O鈧 solution

(Write the content here) Given a 0.35 M K鈧働O鈧 solution, we have the following dissociation reaction: \[K_{3}PO_{4} \rightarrow 3K^{+} + PO_{4}^{3-}\] The stoichiometry shows that for each K鈧働O鈧, we get 3 K鈦 ions and 1 PO鈧劼斥伝 ion. Therefore, the concentrations are: \[ [K^+] = 3 \times 0.35 \mathrm{M} = 1.05 \mathrm{M} \] \[ [PO_{4}^{3-}] = 0.35 \mathrm{M} \]
02

(b) Determine ion concentrations in \(5 \times 10^{-4}\) M CuCl鈧 solution

(Write the content here) Given a \(5 \times 10^{-4}\) M CuCl鈧 solution, we have the following dissociation reaction: \[ CuCl_{2} \rightarrow Cu^{2+} + 2Cl^{-} \] The stoichiometry shows that for each CuCl鈧, we get 1 Cu虏鈦 ion and 2 Cl鈦 ions. Therefore, the concentrations are: \[ [Cu^{2+}] = 5 \times 10^{-4} \mathrm{M} \] \[ [Cl^{-}] = 2 \times (5 \times 10^{-4}) \mathrm{M} = 1 \times 10^{-3} \mathrm{M} \]
03

(c) Determine concentration in 0.0184 M CH鈧僀H鈧侽H solution

(Write the content here) This is a simple molecular solution. There are no ions formed when ethanol (CH鈧僀H鈧侽H) is dissolved in water. So, the concentration of CH鈧僀H鈧侽H in the solution is 0.0184 M.
04

(d) Determine ion concentrations in a mixture of 35.0 mL of 0.010 M Na鈧侰O鈧 and 50.0 mL of 0.200 M K鈧係O鈧

(Write the content here) First, let's find the moles and then the new concentration when the solutions of Na鈧侰O鈧 and K鈧係O鈧 are mixed together. As the volumes are additive, we will consider the total volume for calculating new concentrations. Initial moles of Na鈧侰O鈧: \[ n_{Na_2CO_3} = C_{1}V_{1} = 0.010 \mathrm{M} \times 0.035 \mathrm{L} = 3.5 \times 10^{-4} \text{moles} \] Initial moles of K鈧係O鈧: \[ n_{K_2SO_4} = C_{2}V_{2} = 0.200 \mathrm{M} \times 0.050 \mathrm{L} = 0.01 \text{moles} \] The total volume after mixing: \[ V_{\text{total}} = V_{1} + V_{2} = 35.0 \mathrm{~mL} + 50.0 \mathrm{~mL} = 85.0 \mathrm{~mL} = 0.085 \mathrm{L} \] Now let's find the new concentrations: Concentration of Na鈧侰O鈧: \[ C'_{Na_2CO_3} = \frac{n_{Na_2CO_3}}{V_{total}} = \frac{3.5 \times 10^{-4} \text{moles}}{0.085 \text{L}} = 0.0041 \mathrm{M} \] Concentration of K鈧係O鈧: \[ C'_{K_2SO_4} = \frac{n_{K_2SO_4}}{V_{total}} = \frac{0.010 \text{moles}}{0.085 \text{L}} = 0.118 \mathrm{M} \] Now we have the new concentrations of both salts in the mixed solution. For the Na鈧侰O鈧 dissociation reaction: \[ Na_{2}CO_{3} \rightarrow 2Na^{+} + CO_{3}^{2-} \] We now calculate the ion concentrations: \[ [Na^+] = 2 \times 0.0041 \mathrm{M} = 0.0082 \mathrm{M} \] \[ [CO_{3}^{2-}] = 0.0041 \mathrm{M} \] For the K鈧係O鈧 dissociation reaction: \[ K_{2}SO_{4} \rightarrow 2K^{+} + SO_{4}^{2-} \] We now calculate the ion concentrations: \[ [K^+] = 2 \times 0.118 \mathrm{M} = 0.236 \mathrm{M} \] \[ [SO_{4}^{2-}] = 0.118 \mathrm{M} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Dissociation Reactions
Dissociation reactions are fundamental in understanding how ionic compounds separate in a solution. When an ionic solid, like potassium phosphate ( K鈧働O鈧 ), dissolves in water, it splits into its respective ions. This process is essential for calculating the resulting ion concentrations. Let's take the dissociation of K鈧働O鈧 as an example:
  • The chemical equation for dissociation is K鈧働O鈧 鈫 3K鈦 + PO鈧劼斥伝
  • This means one formula unit of K鈧働O鈧 yields three potassium ions ( K鈦 ) and one phosphate ion ( PO鈧劼斥伝 ).
Understanding stoichiometry in dissociation provides us with the means to predict and calculate the ion concentrations in a solution. Each compound has a characteristic dissociation equation displaying the resulting ions and their ratios, which is crucial for subsequent concentration and stoichiometric calculations.
Solution Concentration Calculations
Calculating the concentration of ions in a solution requires understanding the molarity concept. Molarity ( M ) is the concentration of a solution expressed as moles of solute per liter of solution. For an ionic compound like CuCl鈧 , which dissociates as shown:
  • CuCl鈧 鈫 Cu虏鈦 + 2Cl鈦
This equation tells us that one mole of CuCl鈧 will produce one mole of copper ions ( Cu虏鈦 ) and two moles of chloride ions ( Cl鈦 ). If we have a 5 脳 10^{-4} M solution of CuCl鈧 :
  • The concentration of Cu虏鈦 ions will be 5 脳 10^{-4} M.
  • The concentration of Cl鈦 ions will be 2 脳 (5 脳 10^{-4}) M = 1 脳 10^{-3} M. Each reflects how molarity is used to convert between the overall concentration of the compound and the resulting ions.
These calculations are at the heart of solution stoichiometry and help predict how solutions are prepared and behave.
Stoichiometry in Solutions
Stoichiometry in aqueous solutions involves using the principles of chemical reactions in water. It's about balancing the quantities of reactants and products when solutions are prepared or mixed. Consider a mixture of solutions where Na鈧侰O鈧 and K鈧係O鈧 are mixed:
  • First, calculate the moles of each compound using molarity (M) and volume (L).
  • Combine the molarities by adding to find a new total volume and calculate the resulting concentrations.
For instance, if we mix two solutions: 35.0 mL of 0.010 M Na鈧侰O鈧 and 50.0 mL of 0.200 M K鈧係O鈧 :
  • Calculate the new molarity for each compound using the moles of solute and the total volume (85.0 mL).
  • Apply dissociation equations: Na鈧侰O鈧 鈫 2Na鈦 + CO鈧兟测伝 and K鈧係O鈧 鈫 2K鈦 + SO鈧劼测伝 .
  • Calculate individual ion concentrations by multiplying by their respective coefficients from the dissociation equation.
By doing these stoichiometric calculations, we predict how the ions interact in a mixture to give insights into chemical behavior and reaction progress in solution.

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