Question

Calculate the molarity of a solution containing \(10.0\) grams of sulfuric acid in \(500 \mathrm{ml}\) of solution. (MW of \(\mathrm{H}_{2} \mathrm{SO}_{4}=98.1 .\) )

Short answer

The molarity of the solution containing \(10.0\) grams of sulfuric acid in \(500 \, \mathrm{ml}\) of solution is \(0.204 \, \mathrm{M}\).

Step-by-step solution

Determine the moles of sulfuric acid

To find the moles of sulfuric acid, we will use the formula: moles = mass (grams) / molecular weight. We are given that there are \(10.0\) grams of sulfuric acid and the molecular weight of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is \(98.1\). So the moles of sulfuric acid can be calculated as follows: Moles of sulfuric acid = \(\frac{10.0 \, \text{grams}}{98.1 \, \text{g/mol}}\)

Calculate the moles of sulfuric acid

Now, we will calculate the moles of sulfuric acid: Moles of sulfuric acid = \(\frac{10.0}{98.1} = 0.102 \, \text{moles}\)

Convert the volume of the solution to liters

We are given a volume of \(500 \, \mathrm{ml}\) and we need to convert it into liters by dividing the volume in milliliters by 1000: Volume in liters = \(\frac{500 \, \text{ml}}{1000} = 0.5 \, \text{L}\)

Calculate the molarity of the solution

Now, we have the moles of sulfuric acid and the volume of the solution in liters. We can calculate the molarity using the formula: Molarity = Moles of solute / Volume of solution (L): Molarity of the solution = \(\frac{0.102 \, \text{moles}}{0.5 \, \text{L}}\)

Determine the molarity

Lastly, we will determine the molarity of the solution: Molarity of the solution = \(\frac{0.102}{0.5} = 0.204 \, \text{M}\) So, the molarity of the solution containing \(10.0\) grams of sulfuric acid in \(500 \, \mathrm{ml}\) of solution is \(0.204 \, \mathrm{M}\).

Key concepts

Solution Concentration

Understanding solution concentration is vital in chemistry, as it describes the amount of a substance, known as the solute, present in a specific volume of solvent. The most common way to express concentration in chemistry is molarity, which is measured in moles per liter (mol/L or M). Molarity tells us how many moles of solute are present in one liter of solution.

To calculate molarity, you will need to know the number of moles of the solute present in the solution and the total volume of the solution in liters. Once you have these values, divide the moles of solute by the solution volume:
Molarity (M) = (Moles of solute) / (Volume of solution in liters).

This calculation is fundamental in preparing solutions for various applications in laboratories, industry, and medicine.

Moles of Solute

The mole is a fundamental unit in chemistry that provides a method for expressing the amount of a substance. One mole of any substance contains approximately 6.022 x 10²³ particles, which could be atoms, molecules, ions, or electrons, depending on the substance. This number is known as Avogadro's number.

To calculate the moles of a solute in a solution, divide the mass of the solute (in grams) by its molecular weight (also referred to as molar mass, in grams per mole):
Moles of solute = mass of solute (g) / Molecular weight (g/mol).

Knowing the moles of solute is essential for quantitative reactions and solution preparation. It allows chemists to predict how substances will react quantitatively, which is critical in fields such as pharmacy where precise dosages are necessary.

Molecular Weight

Molecular weight, or molar mass, is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It's calculated by adding up the atomic weights of all atoms present in the molecular formula of the substance, as listed on the periodic table of elements.

For instance, to find the molecular weight of sulfuric acid (H₂SO₄), you add the weights of two hydrogen atoms, one sulfur atom, and four oxygen atoms. Knowing the molecular weight is essential when working with chemical reactions and for converting between moles and grams, which is necessary for preparing solutions with precise molarity.

Volume of Solution

The volume of solution refers to the total space that both the solute and solvent occupy. It is important to express this volume in liters (L) when calculating molarity, because molarity is defined in terms of moles per liter.

If provided with volume in milliliters (mL), a simple conversion is used: 1 L = 1000 mL. Hence, dividing the volume in milliliters by 1000 will give you the volume in liters:
Volume (L) = Volume (mL) / 1000.

Accurate measurement of solution volume is crucial, especially when preparing solutions for titrations, where molarity must be known precisely to determine the concentration of an unknown solution.