Question

What volume of 0.100\(M \mathrm{Na}_{3} \mathrm{PO}_{4}\) is required to precipitate all the lead(II) ions from 150.0 \(\mathrm{mL}\) of 0.250\(M \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Short answer

We need 375 mL of 0.100 M Na3PO4 solution to precipitate all the lead(II) ions from 150.0 mL of 0.250 M Pb(NO3)2 solution.

Step-by-step solution

Calculate the moles of Pb(NO3)2 present in the solution

First, we need to determine the number of moles of Pb(NO3)2 in 150.0 mL of 0.250 M solution. We can find this by using the formula: Moles = (Molarity) × (Volume in Liters) Convert the volume of the solution from mL to L: Volume in Liters = 150.0 mL × (1 L / 1000 mL) = 0.150 L Now, calculate the moles of Pb(NO3)2: Moles of Pb(NO3)2 = (0.250 M) × (0.150 L) = 0.0375 moles

Determine the moles of Na3PO4 required to precipitate all Pb(II) ions

Using the stoichiometry from the balanced equation, we need 1 mole of Na3PO4 for every 1 mole of Pb(NO3)2. So, we require the same number of moles of Na3PO4 as we calculated for Pb(NO3)2. Moles of Na3PO4 required = Moles of Pb(NO3)2 = 0.0375 moles

Calculate the volume of 0.100 M Na3PO4 solution needed

Now, we will find the volume of 0.100 M Na3PO4 solution needed to provide the required moles of Na3PO4. We can use the formula: Volume in Liters = (Moles) / (Molarity) Calculate the volume of Na3PO4 solution needed: Volume of Na3PO4 solution = (0.0375 moles) / (0.100 M) = 0.375 L

Convert the volume to milliliters

Finally, we will convert the volume of Na3PO4 solution from liters to milliliters: Volume in mL = 0.375 L × (1000 mL / 1 L) = 375 mL Thus, we need 375 mL of 0.100 M Na3PO4 solution to precipitate all the lead(II) ions from 150.0 mL of 0.250 M Pb(NO3)2 solution.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. In order to understand stoichiometry, you can think of a balanced chemical equation as a recipe. Just like a recipe tells you the amount of ingredients needed to make a dish, a balanced equation tells you how much of each chemical you need to react together.

When using stoichiometry, we often interpret the coefficients in a balanced chemical equation as the number of moles of each substance. For instance, when using the stoichiometry of the reaction to predict the volume of a reactant needed, we start by calculating the number of moles we have or need. This calculation involves converting concentrations and volumes, as seen in the example problem. Stoichiometry is crucial as it ensures we use the right proportions of chemicals to avoid wastage or insufficient reactions.

Precipitation Reaction

A precipitation reaction occurs when two solutions are combined and an insoluble solid, known as a precipitate, forms. This usually happens when the cations from one solution and the anions from another solution combine to create a compound that is not soluble in water. By observing the formation of a solid precipitate, chemists can confirm a precipitation reaction has occurred.

In the given problem, when sodium phosphate \((\text{Na}_3\text{PO}_4)\) is mixed with lead nitrate \((\text{Pb(NO}_3\text{)}_2)\), a precipitation reaction takes place, forming lead phosphate \((\text{Pb}_3(\text{PO}_4)_2)\) as a solid precipitate. Understanding precipitation reactions is essential because it helps in separating compounds or removing impurities from solutions.

Molarity

Molarity is a way to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution, shown by the symbol \(M\), and is calculated using the formula: \(\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}.\)

Molarity is significant in determining how much of a chemical reactant is present in a solution. In the previous example, knowing that the molarity of the lead nitrate solution is 0.250M allows us to calculate the exact number of moles we have, which is critical for figuring out how much of the other reactant, sodium phosphate, is needed for the reaction. When you dissolve a precise amount of solute in water to make up a desired volume, you create a solution with a specific molarity.

Chemical Reactions

Chemical reactions involve the transformation of substances, where reactants are converted into products. These reactions can be represented by chemical equations. Each substance involved in the reaction is denoted by its chemical formula, and the direction of the reaction is indicated by an arrow.

In the problem example, the chemical reaction taking place is \(\text{3Na}_3\text{PO}_4 + 2\text{Pb(NO}_3\text{)}_2 \rightarrow \text{Pb}_3(\text{PO}_4)_2 + 6\text{NaNO}_3\). This equation showcases the principle of conservation of mass, meaning the number and type of atoms on each side of the equation are the same. Knowing the balanced equation allows us to determine the stoichiometry of the reaction and calculate necessary amounts of reactants and products.