Question

(a) Calculate the molarity of a solution that contains \(0.0250 \mathrm{~mol} \mathrm{NH}_{4} \mathrm{Cl}\) in exactly \(500 \mathrm{~mL}\) of solution. (b) How many moles of \(\mathrm{HNO}_{3}\) are present in \(50.0 \mathrm{~mL}\) of a \(2.50 \mathrm{M}\) solution of nitric acid? (c) How many milliliters of \(1.50 \mathrm{M} \mathrm{KOH}\) solution are needed to provide \(0.275 \mathrm{~mol}\) of KOH?

Short answer

(a) The molarity of the NH₄Cl solution is \(0.0500 \mathrm{M}\). (b) There are \(0.125 \mathrm{~mol}\) of HNO₃ in the 2.50 M solution. (c) \(183.3 \mathrm{~mL}\) of the 1.50 M KOH solution are needed to provide \(0.275 \mathrm{~mol}\) of KOH.

Step-by-step solution

(a) Calculate the molarity

To calculate the molarity (M) of a solution, we use the following formula: \[ M = \frac{n}{V} \] where M is the molarity, n is the number of moles of solute, and V is the volume of the solution in liters. In this case, we have 0.0250 mol of NH₄Cl in 500 mL of solution. First, convert the volume from mL to L: \[ V = \frac{500 \mathrm{~mL}}{1000} = 0.500 \mathrm{~L} \] Now, plug the values into the formula and solve for M: \[ M = \frac{0.0250 \mathrm{~mol}}{0.500 \mathrm{~L}} = 0.0500 \mathrm{M} \]

(b) Calculate the number of moles

To find the number of moles (n) of the solute in a solution, we rearrange the molarity formula: \[ n = M \times V \] In this case, we have a 2.50 M HNO₃ solution and a volume of 50.0 mL. First, convert the volume from mL to L: \[ V = \frac{50.0 \mathrm{~mL}}{1000} = 0.0500 \mathrm{~L} \] Now, plug the values into the formula and solve for n: \[ n = (2.50 \mathrm{M}) \times (0.0500 \mathrm{~L}) = 0.125 \mathrm{~mol} \]

(c) Calculate the volume of a solution

To find the volume (V) of a solution needed to provide a certain number of moles given its molarity, we can rearrange the molarity formula: \[ V = \frac{n}{M} \] In this case, we need 0.275 mol of KOH from a 1.50 M KOH solution. Plug the values into the formula and solve for V in liters: \[ V = \frac{0.275 \mathrm{~mol}}{1.50 \mathrm{M}} = 0.1833 \mathrm{~L} \] Then, convert the volume to mL: \[ V = 0.1833 \mathrm{~L} \times 1000 = 183.3 \mathrm{~mL} \]

Key concepts

Molarity Formula

Molarity is a measurement of the concentration of a solution, representing how many moles of solute are present in one liter of solution. It is a critical concept in chemistry as it allows scientists and students alike to make accurate and consistent measurements of chemical solutions.

The molarity formula, expressed as
\[ M = \frac{n}{V} \]
defines M as molarity, n as the number of moles of solute, and V as the volume of the solution in liters. To utilize the formula correctly, it's important to ensure you convert the volume of the solution to liters if it's given in another unit, like milliliters (mL). This ensures that the units of measurement are consistent, so the calculated molarity is accurate.

When using the molarity formula, a common source of error to watch out for is not converting the volume to the correct units. Also, ensure that the moles of solute align with the actual substance being dissolved, as using incorrect molar masses can lead to inaccurate results.

Moles of Solute

The term 'moles of solute' refers to the amount of a substance (the solute) that is dissolved in a given volume of solvent to create a solution. One mole of any substance contains Avogadro's number of molecules or atoms, which is approximately \(6.022 \times 10^{23}\). Understanding moles is crucial because it allows chemists to count particles by weighing them, bridging the macroscopic world we can measure to the microscopic world of atoms and molecules.

To determine the moles of solute needed for a chemical reaction or to achieve a desired molarity, it's essential to use the molecular weight of the substance in question. For example, if calculating for a glucose solution, the molecular weight of glucose (C6H12O6) would be necessary to convert from grams to moles.

Accurate calculation of the moles of solute is fundamental for preparing solutions of precise concentrations, which is necessary for consistently reproducible results in chemical experimentation and manufacture.

Volume of Solution

The volume of the solution is the measure of the space that the solution occupies. This is typically expressed in liters (L), milliliters (mL), or cubic centimeters (cm³), with 1 mL being equivalent to 1 cm³. For molarity calculations, the solution's volume needs to be in liters to match the molarity's units.

When preparing a solution, you often measure the volume of the solvent added to a certain amount of solute. Precise measurement of the solution's volume is critical because it affects the final concentration of the solution. For instance, when you add water to dissolve sodium chloride to create a saline solution, the total volume after the salt dissolves gives you the volume needed for molarity calculations.

For practical purposes, laboratory equipment like graduated cylinders, pipettes, or burettes are commonly used to measure the volume accurately. When converting from milliliters to liters (which is needed for molarity calculations), remember that there are 1000 milliliters in 1 liter. Care should be taken to ensure that measurements are precise, as even small errors in volume can lead to significant variations in molarity.