Question

Calculate the molarity of a solution prepared by dissolving (a) \(0.17 \mathrm{~mol}\) sulfuric acid in \(85 \mathrm{~mL}\) of solution. (b) \(7.5 \times 10^{-3} \mathrm{~mol}\) of sodium nitrate in a total volume of \(13.5 \mathrm{~mL}\) of solution.

Short answer

The molarity of the sulfuric acid solution is approximately \(2.00\textrm{ M}\). The molarity of the sodium nitrate solution is approximately \(0.556\textrm{ M}\).

Step-by-step solution

- Understand Molarity

Molarity is a measure of the concentration of a solute in a solution and is defined as the number of moles of solute divided by the liters of solution. The formula for molarity (M) is: \( M = \frac{n}{V} \), where \( n \) is the number of moles of the solute and \( V \) is the volume of the solution in liters.

- Calculate the Molarity of Sulfuric Acid

Convert the volume of the solution to liters by dividing by 1000. \( V = \frac{85}{1000} = 0.085 \ L \). Then, use the molarity formula: \( M = \frac{n}{V} = \frac{0.17}{0.085} \) mol/L.

- Calculate the Molarity of Sodium Nitrate

Convert the volume of the solution to liters by dividing by 1000. \( V = \frac{13.5}{1000} = 0.0135 \ L \). Then use the molarity formula: \( M = \frac{n}{V} = \frac{7.5 \times 10^{-3}}{0.0135} \) mol/L.

Key concepts

Solute Concentration

Solute concentration is a key term in chemistry relating to the amount of solute that is dissolved in a specific amount of solution. It refers to the 'strength' or how 'concentrated' the solute is within a mixture. One common measure of solute concentration is molarity, which we often denote with the letter 'M'. Molarity is expressed as the number of moles of solute per liter of solution. It is crucial for accurately and precisely communicating how much of a given substance is present in a mixture, which is fundamental to performing calculations and experiments in chemistry.

Understanding solute concentration is vital when mixing solutions for reactions, calibrating experiments, and predicting the outcome of chemical processes. When a problem asks to calculate molarity, it is directly asking for the solute concentration. A higher molarity corresponds to a higher concentration of solute in the solution, making it more 'concentrated', while a lower molarity indicates a 'dilute' solution with less solute per volume unit.

Moles of Solute

The moles of solute are a fundamental expression of the quantity of a substance present in a chemical reaction or mixture. A mole is a standard unit in chemistry that measures amount of substance. One mole corresponds to Avogadro's number, which is approximately 6.022 x 10²³ particles (atoms, molecules, ions, etc.). This concept is used when converting between grams of a substance and the number of particles it contains. When using molarity, we are concerned with moles because it directly relates the quantitative aspect of solute particles to the volume of solution it is dissolved in.

To determine the molarity of a solution, you need to know the moles of solute present. This could be given to you or you may need to calculate it from the mass and molar mass of the solute. For instance, in the original exercise, the moles of sulfuric acid and sodium nitrate were given, allowing us to proceed directly to calculating molarity by applying the formula \( M = \frac{n}{V} \).

Solution Volume

Solution volume is the amount of space that the combined solute and solvent occupies and it's typically measured in liters when calculating molarity. It's important to always use liters because molarity is defined in terms of moles per liter. If the given volume is in milliliters or another unit, we must convert it to liters to ensure that the units are consistent with the molarity formula.

In the step by step solution to the original exercise, you'll notice the necessity of converting the volume of the solution from milliliters to liters before applying the molarity formula. This is done by dividing the milliliter measure by 1000. Ensuring the correct volume measurement is essential to achieve an accurate molarity calculation. It's worth noting that when we talk about volume in the context of solutions, we are referring to the final total volume of both the solute and the solvent together, not just the volume that the solvent would be without the solute.