Hydrofluoric acid dissolves glass and must be stored in plastic containers. What mass of a \(45 \%(\mathrm{w} / \mathrm{w})\) solution of \(\mathrm{HF}(a q)\) contains \(1.5 \mathrm{~g}\) of \(\mathrm{HF}\) ?

Understanding percentage composition is crucial in chemistry, particularly when dealing with solutions and mixtures. In the context of hydrofluoric acid (HF) dissolving glass, knowing the percentage composition of a solution allows us to determine how much pure substance is within a solution. When we say a solution is 45% w/w HF, it means that out of 100 grams of the solution, 45 grams are hydrofluoric acid, and the remaining 55 grams are other substances, most commonly water.

For students unpacking this concept, an essential observation is that the percentage composition is always based on mass, not volume. This aspect might seem trivial, but it's the key to understanding the property of '45% w/w'. For instance, in a solution with a different w/w percentage, the amount of HF would change proportionally, altering the mass required to obtain a particular amount of HF. This foundational knowledge sets the stage for solving proportions – the next step to mastering solution chemistry.

Solving proportions in chemistry requires setting up a ratio and finding an unknown quantity. Imagine you have a see-saw with weights on each side; you want them to be balanced. Similarly, a proportion ensures that two ratios are in balance. With the HF example, the ratio of HF to the solution mass (45g HF to 100g solution) must be equivalent to the ratio of the desired amount of HF (1.5g) to the total mass of the solution we're trying to find.

To solve the proportion, we cross-multiply to find the unknown value, often denoted as 'x'. Here's the thought process: If 45g of HF corresponds to 100g of solution, how much solution would contain just 1.5g of HF? By calculating cross-products and solving for 'x', we discover the total mass of solution needed. This problem-solving method is vital in various areas of chemistry, especially when preparing solutions or diluting concentrations.

The mass of solution calculation ties together the concepts of percentage composition and solving proportions. Once the proportion is set up, the calculation leads to the discovery of the total mass of the solution. In our HF problem, after cross-multiplying, we divide both sides of the equation by 45g, simplifying to find the unknown mass 'x' of the solution required to have exactly 1.5 grams of HF.

Here's the calculation broken down: \( x = \frac{1.5g \times 100g}{45g} \). By performing this calculation, students can find out that the total mass of the solution is about 3.33 grams. This is not just a simple math exercise; it's a practical tool used in laboratories across the world. Whether a scientist is creating a buffer solution or a student is conducting an experiment in class, the ability to precisely calculate the mass of a solution is indispensable in the application of chemistry.