Question

A solution is made by dissolving \(49 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in \(250 \mathrm{~mL}\) of water. The molarity of the solution prepared is (a) \(2 \mathrm{M}\) (b) \(1 \mathrm{M}\) (c) \(4 \mathrm{M}\) (d) \(5 \mathrm{M}\)

Short answer

The molarity of the solution prepared is \(2 \mathrm{M}\).

Step-by-step solution

- Convert Mass of Solute to Moles

To find molarity, we need to know the moles of solute. The molar mass of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) is \(2 \times 1.01 + 32.07 + 4 \times 16.00 = 98.08 \mathrm{~g/mol}\). The number of moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) is calculated by dividing the mass of the acid by its molar mass: \[\text{Moles of } \mathrm{H}_{2}\mathrm{SO}_{4} = \frac{49 \mathrm{~g}}{98.08 \mathrm{~g/mol}} \approx 0.5 \mathrm{~mol}\]

- Convert Volume of Solvent to Liters

Molarity is defined as moles of solute per liter of solution. First, convert the volume from milliliters to liters by dividing by 1000: \[\text{Volume of solution in liters} = \frac{250 \mathrm{~mL}}{1000} = 0.25 \mathrm{~L}\]

- Calculate Molarity

Now, calculate the molarity by dividing the moles of solute by the volume of solution in liters: \[\text{Molarity} = \frac{\text{Moles of } \mathrm{H}_{2}\mathrm{SO}_{4}}{\text{Volume of solution in liters}} = \frac{0.5 \mathrm{~mol}}{0.25 \mathrm{~L}} = 2 \mathrm{M}\]

Key concepts

Moles of Solute

When dealing with chemical solutions, one of the fundamental concepts is the moles of solute, which refers to the amount of a substance present in a solution. A mole is a unit in chemistry that represents a very large number of particles, specifically Avogadro's number, which is approximately 6.022 x 10^23 particles. This number is chosen because it's the number of atoms in exactly 12 grams of carbon-12, which ties atomic masses on the periodic table to a measurable quantity of substance.

To calculate the moles of solute, divide the mass of the solute (in grams) by its molar mass (in grams per mole). The molar mass is the weight of one mole of a substance and is usually measured in grams per mole (\text{g/mol}). Here's a simple equation to remember:
\[\text{Moles of solute} = \frac{\text{Mass of solute (g)}}{\text{Molar mass (g/mol)}}\]
In our example, we had a mass of 49 g of \text{H}_2\text{SO}_4. By calculating the moles, we understand the actual number of molecules involved in the reaction, which is critical for predicting the outcome of chemical processes.

Molar Mass

The concept of molar mass is pivotal in converting between the mass of a substance and the number of moles. The molar mass of a compound is obtained by summing the individual molar masses of each element multiplied by its number of atoms in one molecule of the compound. For instance, sulfuric acid (\text{H}_2\text{SO}_4) comprises two hydrogen atoms, one sulfur atom, and four oxygen atoms. To calculate its molar mass, we would consider the molar masses of hydrogen (1.01 g/mol), sulfur (32.07 g/mol), and oxygen (16.00 g/mol), derived from the periodic table.

The calculation takes the form:
\[\text{Molar mass of } \text{H}_2\text{SO}_4 = (2 \times 1.01) + 32.07 + (4 \times 16.00) \text{ g/mol} = 98.08 \text{ g/mol}\]
Understanding the molar mass allows for accurate measurements in chemical reactions, ensuring that the stoichiometry, or the proportion of reactants, is correct, which is crucial for expected results.

Solutions and Concentrations

In chemistry, solutions and concentrations play a key role. A solution is a homogeneous mixture of two or more substances. The substance in the largest amount is called the solvent, and the substance in the smaller amount is called the solute. When we discuss a chemical solution, we often want to know how concentrated it is – this is where the concept of molarity comes into play.

Molarity (M) is defined as the number of moles of solute per liter of solution. It is a measure of the concentration of a solute in a solution, or of any chemical species, in terms of amount of substance in a given volume. The formula for molarity is:
\[\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters (L)}}\]
For example, by taking the previously calculated 0.5 moles of \text{H}_2\text{SO}_4 and dividing by the volume of the solution (0.25 liters), we get the concentration of sulfuric acid in the solution to be 2 M. This concentration informs us how many moles of the solute are present in each liter of solution, which is essential for quantitative analysis and for procedures like dilutions and titrations.