Question

Calculate the molarity of each of these solutions. a. \(A 5.623-g\) sample of \({NaHCO}_{3}\) is dissolved in enough water to make 250.0 \({mL}\) of solution. b. A \(184.6-{mg}\) sample of \({K}_{2} {Cr}_{2} {O}_{7}\) is dissolved in enough water to make 500.0 \({mL}\) of solution. c. A 0.1025 -g sample of copper metal is dissolved in 35 \({mL}\) of concentrated \({HNO}_{3}\) to form \({Cu}^{2+}\) ions and then water is added to make a total volume of 200.0 \({mL}\) . (Calculate the molarity of \({Cu}^{2+} . )\)

Short answer

The molarity of the solutions are as follows: a. The molarity of the \(NaHCO_3\) solution is \(0.268\) mol/L. b. The molarity of the \(K_2Cr_2O_7\) solution is \(0.001256\) mol/L. c. The molarity of the \(Cu^{2+}\) solution is \(0.008065\) mol/L.

Step-by-step solution

Calculating the moles of \(NaHCO_3\)

First, calculate the molar mass of \(NaHCO_3\): Na=22.99 g/mol, H=1.01 g/mol, C=12.01 g/mol, and O=16.00 g/mol, so the molar mass of \(NaHCO_3\) = 22.99 + 1.01 + 12.01 + 3*16.00 = 84.01 g/mol. Now, divide the given mass of \(NaHCO_3\) (5.623 g) by its molar mass (84.01 g/mol) to find the moles of solute: moles = 5.623 g / 84.01 g/mol ≈ 0.067 mole.

Convert the volume of the solution to liters

The volume of the solution is given as 250.0 mL. Convert this to liters by dividing by 1000 mL/L: 250.0 mL * (1 L / 1000 mL) = 0.250 L.

Calculate the molarity

Now, divide the moles of solute by the volume of the solution (in liters) to find the molarity: molarity = \(0.067\) moles / \(0.250\) L ≈ 0.268 mol/L. The molarity of the \(NaHCO_3\) solution is \(0.268\) mol/L. #b. Calculate the molarity of the \(K_2Cr_2O_7\) solution.#

Calculating the moles of \(K_2Cr_2O_7\)

Calculate the molar mass of \(K_2Cr_2O_7\): K=39.10 g/mol, Cr=51.99 g/mol, and O=16.00 g/mol, so the molar mass of \(K_2Cr_2O_7\) = 2*39.10 + 2*51.99 + 7*16.00 = 294.18 g/mol. Convert the given mass of \(K_2Cr_2O_7\) (184.6 mg) to grams by dividing by 1000 mg/g: 184.6 mg * (1 g / 1000 mg) = 0.1846 g. Now, divide the mass of \(K_2Cr_2O_7\) (0.1846 g) by its molar mass (294.18 g/mol) to find the moles of solute: moles = 0.1846 g / 294.18 g/mol ≈ 0.000628 mole.

Convert the volume of the solution to liters

The volume of the solution is given as 500.0 mL. Convert this to liters by dividing by 1000 mL/L: 500.0 mL * (1 L / 1000 mL) = 0.500 L.

Calculate the molarity

Now, divide the moles of solute by the volume of the solution (in liters) to find the molarity: molarity = \(0.000628\) moles / \(0.500\) L ≈ 0.001256 mol/L. The molarity of the \(K_2Cr_2O_7\) solution is \(0.001256\) mol/L. #c. Calculate the molarity of the \(Cu^{2+}\) solution.#

Calculating the moles of \(Cu\)

Calculate the molar mass of \(Cu\): Cu=63.55 g/mol. Now, divide the given mass of \(Cu\) (0.1025 g) by its molar mass (63.55 g/mol) to find the moles of solute: moles = 0.1025 g / 63.55 g/mol ≈ 0.001613 mole.

Convert the volume of the solution to liters

The final volume of the solution is given as 200.0 mL. Convert this to liters by dividing by 1000 mL/L: 200.0 mL * (1 L / 1000 mL) = 0.200 L.

Calculate the molarity of the \(Cu^{2+}\) ions

Now, divide the moles of \(Cu^{2+}\) ions by the volume of the solution (in liters) to find the molarity: molarity = \(0.001613\) moles / \(0.200\) L ≈ 0.008065 mol/L. The molarity of the \(Cu^{2+}\) solution is \(0.008065\) mol/L.

Key concepts

Solutions

In chemistry, solutions are crucial in various experiments and everyday use. A solution is a homogeneous mixture of two or more substances. The substance in the largest amount is called the solvent, typically a liquid, while the substance in smaller amounts is the solute, which may be a solid, liquid, or gas. When a solute dissolves in a solvent, it creates a single-phase solution, meaning it looks uniform throughout.
For example, in the provided exercises, water acts as the solvent, and substances like sodium bicarbonate \( (NaHCO_3) \) and potassium dichromate \( (K_2Cr_2O_7) \) are the solutes.
The concentration of solutions is commonly expressed in terms of molarity, which is the measure of moles of solute per liter of solution. This concept helps scientists and students understand how much of a substance is present in a specific volume of solution.

• Solution: A homogeneous mixture of two or more substances.
• Solvent: Substance in the largest amount; often a liquid.
• Solute: Substance in smaller amount; can be solid, liquid, or gas.
• Molarity: Number of moles of solute per liter of solution.

Mole Calculations

The mole is a fundamental concept in chemistry that provides a link between the atomic scale and the macroscopic world. It represents a specific number — Avogadro's number, which is approximately \(6.022 \times 10^{23}\). When dealing with chemical substances, moles allow us to convert between mass and number of molecules or atoms.
To find molarity, first, we need to understand how to calculate the number of moles of a given substance.
The step-by-step process includes:- Determine the molar mass of the solute, which is calculated by summing the atomic masses of all atoms in the molecule. For instance, in sodium bicarbonate \( (NaHCO_3) \), its molar mass can be calculated using the atomic masses of \(Na\), \(H\), \(C\), and \(O\). - Convert the mass of the solute into moles using the formula: \[ \text{moles} = \frac{\text{mass of solute (in grams)}}{\text{molar mass (in g/mol)}} \]Mole calculations are vital as they allow us to determine the exact quantity of substance involved in a reaction or contained in a solution.

• Molar mass: Sum of atomic masses in a molecule.
• 1 mole: \(6.022 \times 10^{23}\) particles (Avogadro's Number).
• Moles: Convert mass to moles using molar mass.

Volume Conversions

When working with solutions, we often need to convert units of volume to find molarity. Volume conversions are straightforward but essential when calculating molarity, which involves liters as the standard unit for solution volume.
Most laboratory measurements of solutions begin in milliliters (mL). Since molarity is expressed in moles per liter, we need to convert milliliters to liters. The conversion factor for this is simple:1 liter (L) = 1000 milliliters (mL).
For example, to convert 250 mL to liters, divide by 1000:\[ 0.250 \text{ L} = \frac{250 \text{ mL}}{1000} \]This conversion is necessary to ensure molarity calculations are correct, as illustrated in the exercise problems. Precise volume measurements are critical in lab settings to ensure accurate solution concentrations.

• Convert mL to L by dividing by 1000.
• Use liters for molarity calculations.
• Precise measurements ensure accurate results.