Question

Determine the resulting nitrate ion concentration when \(95.0 \mathrm{~mL}\) of \(0.992 \mathrm{M}\) potassium nitrate and \(155.5 \mathrm{~mL}\) of \(1.570 \mathrm{M}\) calcium nitrate are combined.

Short answer

The resulting nitrate ion concentration is 2.325 M.

Step-by-step solution

Understand the Problem

We are tasked with finding the nitrate ion concentration when two solutions are mixed: potassium nitrate and calcium nitrate. Each provides nitrate ions to the solution.

Calculate Moles of Nitrate from Potassium Nitrate

Potassium nitrate ( ext{KNO}_3) provides one nitrate ion per formula unit. Calculate the moles of ext{KNO}_3 using \[\text{moles} = C \times V = 0.992 \mathrm{~M} \times 0.095 \mathrm{~L} = 0.09424 \,\text{mol}\]This is also the moles of nitrate ions from potassium nitrate.

Calculate Moles of Nitrate from Calcium Nitrate

Calcium nitrate ( ext{Ca(NO}_3 ext{)}_2) provides two nitrate ions per formula unit. Calculate the moles of ext{Ca(NO}_3 ext{)}_2 using\[\text{moles} = C \times V = 1.570 \mathrm{~M} \times 0.1555 \mathrm{~L} = 0.244135 \,\text{mol}\]Since each mole of calcium nitrate provides two nitrate ions, the moles of nitrate from calcium nitrate are:\[0.244135 \,\text{mol} \times 2 = 0.48827 \,\text{mol}\]

Calculate Total Nitrate Moles

Add the moles of nitrate ions from both sources:\[\text{Total moles of nitrate} = 0.09424 \,\text{mol} + 0.48827 \,\text{mol} = 0.58251 \,\text{mol}\]

Calculate Total Solution Volume

The total volume of the mixed solution is the sum of the two volumes:\[95.0 \,\text{mL} + 155.5 \,\text{mL} = 250.5 \,\text{mL}\]Convert to liters for molarity calculation:\[250.5 \,\text{mL} = 0.2505 \,\text{L}\]

Calculate Nitrate Ion Concentration

Determine the concentration of nitrate ions by dividing the total moles by the total volume:\[\text{Nitrate ion concentration} = \frac{0.58251 \,\text{mol}}{0.2505 \,\text{L}} = 2.325 \,\text{M}\]

Key concepts

Potassium Nitrate

Potassium nitrate, often denoted as KNO extsubscript{3}, is a chemical compound consisting of potassium, nitrogen, and oxygen. It's not just important in chemistry, but also widely used in fertilizers, food preservation, and even fireworks. When studying solutions, potassium nitrate is a key player because it contributes nitrate ions ( ext{NO} extsubscript{3} extsuperscript{-}) upon dissociation in water. This means every molecule of potassium nitrate provides one nitrate ion, which is significant in solution chemistry.
Understanding how it dissociates helps in calculating how many nitrate ions will be present in a solution. For instance, if you have a solution with a known concentration of potassium nitrate, you can directly calculate the moles of nitrate ions produced, as one mole of KNO extsubscript{3} equals one mole of nitrate ions.

Calcium Nitrate

Calcium nitrate, represented as Ca(NO extsubscript{3} extsubscript{2}), is another invaluable compound in chemistry. It contains calcium and two nitrate ions in its structure. This compound is more complex compared to potassium nitrate because it provides two nitrate ions per formula unit instead of just one.
This feature makes it critically important when calculating total nitrate concentrations in mixed solutions. When you dissolve calcium nitrate in water, each formula unit generates two nitrate ions. This aspect must be considered for accurate molarity calculations, as evidenced in the previous exercise. To find the moles of nitrate ions derived from calcium nitrate, multiply the moles of calcium nitrate by two.

Solution Mixing

When it comes to mixing solutions, like in the exercise where potassium nitrate and calcium nitrate solutions are combined, understanding the resultant chemical behavior is essential. Mixing involves simply combining the volumes and the chemical reactions of the substances. Here, no new chemical reactions occur; rather, the solutions share their components, like nitrate ions, in a common solvent, typically water.
The overall task is to determine the final concentration of the mixed components, particularly the nitrate ions in this case. Knowing and applying the properties of each solute helps predict the behavior of the solution after mixing. As demonstrated with potassium nitrate and calcium nitrate, you must calculate the contributions of nitrate ions from each solution separately before mixing. Then, combine these contributions to find the total nitrate concentration in the resulting solution.

Molarity Calculation

Molarity is a useful concept in chemistry because it describes the concentration of a solute in a solution. It's expressed in moles of solute per liter of solution ( ext{mol/L}). For the exercise with potassium nitrate and calcium nitrate, knowing how to calculate molarity is critical.
To determine the molarity of nitrate ions in a solution, you must divide the total moles of nitrate ions obtained by the volume of the solution in liters. This process involves several steps: first, calculate the moles of nitrate ions each compound contributes, as shown with KNO extsubscript{3} providing one nitrate ion per mole and Ca(NO extsubscript{3} extsubscript{2}) providing two. Then, sum these moles to get a total, and finally, divide by the total solution volume in liters to get the nitrate ion concentration.
This method ensures accuracy in determining the concentration, which is essential for further chemical reactions and analyses.