Question

After \(125.0 \mathrm{~mL}\) of water is added to \(50.0 \mathrm{~mL}\) of a \(0.250 \mathrm{M}\) solution of ammonium phosphate, (a) what is the molar concentration of ammonium phosphate in the diluted solution? Once in solution, the ammonium phosphate exists not as intact ammonium phosphate but rather as ammonium ions and phosphate ions. What are the molar concentrations (b) of ammonium ions in the diluted solution and (c) of phosphate ions in the diluted solution?

Short answer

The molar concentration of ammonium phosphate in the diluted solution is \(0.0714M\). The molar concentration of ammonium ions (\(NH_4^+\)) in the diluted solution is \(0.214M\), and the molar concentration of phosphate ions (\(PO_4^{3-}\)) in the diluted solution is \(0.0714M\).

Step-by-step solution

Identify the formula for dilution

The formula for dilution is given by: \[C_1V_1=C_2V_2\] Where: \(C_1\) is the initial concentration of the solution \(V_1\) is the initial volume of the solution \(C_2\) is the final concentration of the solution \(V_2\) is the final volume of the solution

Calculate the final concentration (diluted)

Given that \(C_1 = 0.250M\), \(V_1 = 50.0mL\), and \(V_2 = 125.0mL + 50.0mL = 175.0mL\). Substitute these values into the formula and solve for \(C_2\): \[(0.250M)(50.0mL)=(C_2)(175.0mL)\] To find \(C_2\), divide both sides by \(175.0mL\): \[C_2 = \frac{(0.250M)(50.0mL)}{175.0mL} = 0.0714M\] Therefore, the molar concentration of ammonium phosphate in the diluted solution is \(0.0714M\).

Find the dissociation equation for ammonium phosphate

The dissociation equation for ammonium phosphate (\(NH_4)_3PO_4\)) is as follows: \((NH_4)_3PO_4 \rightarrow 3NH_4^+ + PO_4^{3-}\)

Calculate molar concentrations of ammonium ions in the diluted solution (b)

From the dissociation equation, there are 3 moles of ammonium ions (\(NH_4^+\)) for every 1 mole of ammonium phosphate. Therefore, the molar concentration of ammonium ions in the diluted solution is: \[0.0714M \times 3 = 0.214M\] Thus, the molar concentration of ammonium ions in the diluted solution is \(0.214M\).

Calculate molar concentrations of phosphate ions in the diluted solution (c)

From the dissociation equation, there is 1 mole of phosphate ions (\(PO_4^{3-}\)) for every 1 mole of ammonium phosphate. Therefore, the molar concentration of phosphate ions in the diluted solution is: \[0.0714M \times 1 = 0.0714M\] Thus, the molar concentration of phosphate ions in the diluted solution is \(0.0714M\).

Key concepts

Dilution Calculation

Understanding dilution calculations is crucial when working with chemical solutions. Dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. For students working through problems such as determining the molar concentration after dilution, it's essential to grasp the underlying principle.

One of the fundamental formulas used in dilution problems is the equation: \[C_1V_1=C_2V_2\]. This formula represents the relationship between the concentrations and volumes before and after dilution. Here's what each variable stands for:

• \(C_1\): Initial molar concentration of the solution.
• \(V_1\): Initial volume of the solution.
• \(C_2\): Final molar concentration after dilution.
• \(V_2\): Final volume after water or another solvent is added.

When you combine this with a step-by-step approach to solving the problem, you can calculate any unknown in the equation.

Chemical Dissociation

Chemical dissociation is when a compound breaks down into smaller chemicals or ions when dissolved in a solvent. This process is ubiquitous in the realm of aqueous solutions, and understanding it aids in predicting the behavior of solutes such as ammonium phosphate in water.

The dissociation equation gives a clear picture of the ion formation from the solute. In the case of ammonium phosphate, represented by the formula \((NH_4)_3PO_4\), the dissociation in water can be written as:\[(NH_4)_3PO_4 \rightarrow 3NH_4^+ + PO_4^{3-}\].This signifies that one formula unit of ammonium phosphate will produce three ammonium ions and one phosphate ion upon dissolution. Knowing this ratio is key to finding out the concentration of each ion in the solution after dilution.

Ammonium Phosphate

Ammonium phosphate is a compound with the formula \((NH_4)_3PO_4\), often used as a fertilizer for its high nitrogen content. In chemistry problems regarding ammonium phosphate, we often look at its behavior in aqueous solutions. As it dissolves, it undergoes chemical dissociation into ammonium ions (\(NH_4^+\)) and phosphate ions (\(PO_4^{3-}\)).

It's vital for students to know this compound's molar mass and how it dissociates in water to solve related exercises. Moreover, as ammonium phosphate dissociates into multiple ions, understanding stoichiometry – the calculation of relative quantities of reactants and products in chemical reactions – is fundamental to solving concentration problems after dilution.

Solution Concentration

The concentration of a solution is a measure of the amount of solute present in a given quantity of solvent. In chemistry, molar concentration, also known as molarity, is frequently used and is denoted by \(M\). It's defined as the number of moles of solute per liter of solution.

• A higher molar concentration means there is more solute in the solution.
• A lower molar concentration indicates a more diluted solution.

It’s imperative to accurately calculate the molar concentration when preparing solutions in a lab or solving textbook problems. An understanding of molar concentration can guide students through exercises that involve predicting the effects of dilution on solution concentration, as well as stoichiometry calculations to find out the concentration of individual ions after dissociation.