Question

Calculate the mass of anhydrous \(\mathrm{HCl}\) in \(10 \mathrm{~mL}\) of concentrated \(\mathrm{HCl}\) (density \(=1.2 \mathrm{~g} / \mathrm{mL}\) ) solution having \(37 \% \mathrm{HCl}\) by weight. (a) \(4.44 \mathrm{~g}\) (b) \(4.44 \mathrm{mg}\) (c) \(4.44 \times 10^{-3} \mathrm{mg}\) (d) \(0.444 \mu \mathrm{g}\)

Short answer

4.44 g

Step-by-step solution

Calculate the mass of the solution

First, find the mass of the entire solution using its density and volume. The mass (m) of the solution can be calculated by using the formula: mass = density × volume. Here the density is 1.2 g/mL and the volume is 10 mL. Therefore, the mass of the solution is 1.2 g/mL × 10 mL = 12 g.

Calculate the mass of \(\mathrm{HCl}\) in the solution

Knowing that the solution is 37% \(\mathrm{HCl}\) by weight, you can find the mass of \(\mathrm{HCl}\) by taking 37% of the total mass of the solution. Calculate the mass of \(\mathrm{HCl}\) as follows: \(0.37 × 12 \text{g} = 4.44 \text{g}\).

Choose the correct answer

Compare the calculated mass of \(\mathrm{HCl}\) with the given options and select the one that matches the calculated mass. The mass of \(\mathrm{HCl}\) is 4.44 g, which corresponds to option (a).

Key concepts

Stoichiometry

Stoichiometry is like the recipe for chemistry, telling us how much of each ingredient we need for the reactions to cook up perfectly. It is the study of the quantitative relationships, or ratios, between the reactants and products in a chemical reaction. For instance, if a cake recipe calls for 2 eggs per cake, and you want to make 3 cakes, you'll need 6 eggs. In chemistry, if a reaction requires 2 molecules of hydrogen gas (H2) to react with 1 molecule of oxygen gas (O2) to produce 2 molecules of water (H2O), stoichiometry can help us calculate exactly how much hydrogen and oxygen we need to make a desired amount of water.

When solving problems in stoichiometry, it is crucial to begin with a balanced chemical equation and use mole ratios to relate the amounts of reactants to products. These relationships help chemists convert from one unit of measure to another, such as from mass to moles or from moles to particles. In our exercise, stoichiometry principles are applied to determine the amount of anhydrous HCl in a solution based on its concentration and volume.

Chemical Solution Concentration

Imagine you’re making lemonade. You mix a certain amount of lemon juice with water. The 'concentration' is how lemony your lemonade is. It's the same in chemistry. The concentration of a solution tells you how much solute (like your lemon juice) is packed into a solvent (like water).

In chemistry, concentration is expressed as the amount of substance per defined space. One common method to express concentration is by percentage weight, which is the mass of the solute divided by the total mass of the solution, multiplied by 100%. This allows chemists to quickly understand the composition of a solution. In our textbook exercise, we were given that the solution is 37% HCl by weight, which means that for every 100 grams of this solution, 37 grams are HCl and the rest is typically water or other substances.

Density and Mass Relationships

Ever wondered why some things float while others sink? That's about 'density'. Density represents how tightly packed the matter in a substance is. It’s determined by dividing the mass of an object by its volume, often expressed in grams per milliliter (g/mL) for liquids.

In practical chemistry, understanding the relationship between density, mass, and volume allows us to measure out substances without having to count every single molecule. If we know the density of a liquid and the volume we have, we can calculate its mass. That's exactly what we did in our problem: we took the known volume of our HCl solution (10 mL) and its density (1.2 g/mL) and used the formula 'mass = density × volume' to find the total mass of the solution. From there, we could use the percentage concentration to find out how much of that mass was just the HCl, the solute in our solution.