Question

Calculate the molarity of each of the following solutions. (a) \(6.30 \mathrm{~g} \mathrm{HNO}_{3}\) dissolved in \(255 \mathrm{~mL}\) of solution (b) \(49.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{SO}_{4}\) dissolved in \(125 \mathrm{~mL}\) of solution (c) \(2.80 \mathrm{~g} \mathrm{KOH}\) dissolved in \(525 \mathrm{~mL}\) of solution (d) \(7.40 \mathrm{~g} \mathrm{Ca}(\mathrm{OH})_{2}\) dissolved in \(200.0 \mathrm{~mL}\) of solution

Short answer

The molarities of the solutions are: (a) 0.3922 M, (b) 4 M, (c) 0.0952 M, (d) 0.5 M

Step-by-step solution

Calculation for solution (a)

Firstly, find the molar mass of HNO3, which is 63.01 g/mol. Next, convert 6.30 g of HNO3 into moles: 6.30 g / 63.01 g/mol = 0.1 mol. Then, convert 255 mL of solution into liters: 255 mL * (1 L / 1000 mL) = 0.255 L. Use the formula Molarity = Moles of solute / Volume of solution in liters to find the molarity: 0.1 mol / 0.255 L = 0.3922 M.

Calculation for solution (b)

Firstly, find the molar mass of H2SO4, which is 98.08 g/mol. Next, convert 49.0 g of H2SO4 into moles: 49.0 g / 98.08 g/mol = 0.5 mol. Then, convert 125 mL of solution into liters: 125 mL * (1 L / 1000 mL) = 0.125 L. Use the formula Molarity = Moles of solute / Volume of solution in liters to find the molarity: 0.5 mol / 0.125 L = 4 M.

Calculation for solution (c)

Firstly, calculate the molar mass of KOH, which is 56.11 g/mol. Then, convert 2.80 g of KOH into moles: 2.80 g / 56.11 g/mol = 0.05 mol. Afterwards, convert 525 mL of solution into liters: 525 mL * (1 L / 1000 mL) = 0.525 L. Use the formula Molarity = Moles of solute / Volume of solution in liters to find the molarity: 0.05 mol / 0.525 L = 0.0952 M.

Calculation for solution (d)

Firstly, find the molar mass of Ca(OH)2, which is 74.10 g/mol. Then, convert 7.40 g of Ca(OH)2 into moles: 7.40 g / 74.10 g/mol = 0.1 mol. Afterwards, convert 200 mL of solution into liters: 200 mL * (1 L / 1000 mL) = 0.2 L. Use the formula Molarity = Moles of solute / Volume of solution in liters to find the molarity: 0.1 mol / 0.2 L = 0.5 M.

Key concepts

Moles of Solute

Understanding the concept of 'moles of solute' is essential when dealing with chemical solutions and their concentrations. First, to determine the moles of a solute in a solution, you need to know its mass and its molar mass. The molar mass is the weight of one mole of a substance, typically expressed in g/mol, and represents the sum of the atomic masses of all the atoms in a molecule of that substance.

To calculate the moles of solute, use the formula:

• Moles = Mass (g) / Molar Mass (g/mol)

For example, if you have 6.30 g of \(\text{HNO}_3\), and its molar mass is 63.01 g/mol, dividing the mass by the molar mass gives you the moles: \[\frac{6.30\, \text{g}}{63.01\, \text{g/mol}} = 0.1\, \text{mol}\]This step is crucial as determining the number of moles allows you to calculate other properties of the solution, such as its molarity.

Volume of Solution

When discussing the concentration of solutions, 'volume of solution' is a key term. It refers to the total volume in which the solute is dissolved, often measured in liters for the purpose of calculating molarity.

It’s essential to convert volumes given in milliliters (mL) to liters (L) because molarity is expressed in moles per liter. The conversion is straightforward as 1 liter = 1000 milliliters. To convert, simply multiply the volume in milliliters by the conversion factor:

• Volume (L) = Volume (mL) × (1 L / 1000 mL)

For instance, for a solution with a volume of 255 mL, converting to liters involves:\[255 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.255 \text{ L}\]
By ensuring the volume is in the correct unit, it becomes possible to utilize it for calculations involving molarity.

Molar Mass

The molar mass is a fundamental concept in chemistry that relates to the weight of one mole of a given substance. Every element in the periodic table has an atomic mass, which can be found on the table. The molar mass of a compound is the sum of the atomic masses of all the atoms in its chemical formula, measured in grams per mole (g/mol).

Calculating the molar mass involves identifying the chemical formula of the compound and summing the atomic masses of each element involved. For example:- For \(\text{HNO}_3\), calculate as follows: - Hydrogen (H): 1.01 g/mol
- Nitrogen (N): 14.01 g/mol
- Oxygen (O, 3 atoms): 16.00 g/mol × 3
The molar mass of \(\text{HNO}_3\) would be:\[1.01 + 14.01 + (16.00\, \times\, 3) = 63.01 \text{ g/mol}\]
This calculated molar mass is used in determining the moles of solute and hence the concentration of the solution in molarity calculations.