Problem 39 - Chemistry The Central Science In Si Units

Question

(a) Calculate the mass percentage of \(\mathrm{NaNO}_{3}\) in a solution containing \(13.6 \mathrm{~g}\) of \(\mathrm{NaNO}_{3}\) in \(834 \mathrm{~g}\) of water. (b) An alloy contains \(2.86 \mathrm{~g}\) of chromium per \(100 \mathrm{~kg}\) of alloy. What is the concentration of chromium in ppm?

Step-by-Step Solution

Answer

(a) 1.60% of \(\mathrm{NaNO}_{3}\), (b) 28.6 ppm chromium.

Step 1: Understanding Mass Percentage Formula

The mass percentage is calculated using the formula: \( \text{Mass % of component} = \left( \frac{\text{mass of the component}}{\text{total mass of the solution}} \right) \times 100 \). In this case, the solution consists of 13.6 g of \( \mathrm{NaNO}_{3} \) and 834 g of water.

Step 2: Calculating Total Mass of Solution

To find the total mass of the solution, add the mass of \( \mathrm{NaNO}_{3} \) to the mass of water: \( 13.6 \text{ g} + 834 \text{ g} = 847.6 \text{ g} \).

Step 3: Calculate Mass Percentage of NaNO3

Using the total mass calculated, find the mass percentage of \( \mathrm{NaNO}_{3} \) as follows: \( \frac{13.6}{847.6} \times 100 \approx 1.60\% \). This is the mass percentage of sodium nitrate in the solution.

Step 4: Understanding Parts Per Million (ppm)

Parts per million (ppm) is calculated using the formula: \( \text{ppm} = \left( \frac{\text{mass of the solute}}{\text{total mass of the solution}} \right) \times 10^6 \). Here, we calculate the ppm of chromium in the alloy.

Step 5: Converting Total Mass of Alloy to Grams

The total mass of the alloy is given as 100 kg. Convert this to grams: \( 100 \text{ kg} = 100,000 \text{ g} \).

Step 6: Calculate Concentration of Chromium in ppm

Using the ppm formula: \( \frac{2.86}{100,000} \times 10^6 = 28.6 \text{ ppm} \). Thus, the concentration of chromium in the alloy is 28.6 ppm.

Key Concepts

Mass Percentage

Mass percentage is a way of expressing a component's concentration in a mixture or solution. It's incredibly helpful in chemistry to determine how much of a specific substance is present in a solution compared to the total amount of all substances in that solution. Here's how you can calculate it:

• First, you need the mass of the component you are interested in. In our example, this is the mass of sodium nitrate (\(\mathrm{NaNO}_3\)).
• Second, find the total mass of the solution. This includes the mass of the water plus the \(\mathrm{NaNO}_3\) in the solution.
• Use the formula: \( \text{Mass \,\%} = \left(\frac{\text{mass of component}}{\text{total mass of solution}}\right) \times 100\)

In the exercise, this gave us a mass percentage of 1.60% for \(\mathrm{NaNO}_3\), which means that out of the entire solution's mass, 1.60% is sodium nitrate.

Parts Per Million

Parts per million (ppm) is another method to express concentration, often used for very dilute solutions or trace amounts of a substance in a mixture. It essentially tells you how many parts of the solute exist in one million parts of the total solution.

• The formula is: \( \text{ppm} = \left( \frac{\text{mass of the solute}}{\text{total mass of the solution}} \right) \times 10^6 \)
• Ppm is particularly useful in fields like environmental science, where you monitor pollutants. It gives a clearer picture for very small concentrations that are hard to express as percentages.

For instance, in the given problem, chromium represents a tiny fraction of the alloy's mass. Converting the total mass from kilograms to grams first helps apply the ppm formula, resulting in a concentration of 28.6 ppm for chromium. This effectively means there are 28.6 grams of chromium per million grams of the alloy.

Solution Composition

Understanding the composition of a solution involves determining what substances it contains and in what proportions. Whether you're dealing with chemical solutions, alloys, or any other mixtures, knowing the composition is key.

• A solution is a homogeneous mixture composed of two or more substances. In a solution, the solute is the substance present in a smaller amount, and the solvent is the substance in greater amount.
• The importance of knowing solution composition is that it allows you to predict and control how the solution behaves. This includes reactions with other chemicals, impacts on health, or industrial applications.
• Different measures tell us different things about the solution. Mass percentage and ppm are both ways to quantify the concentration of components.

This comprehension aids industries from pharmaceuticals to environmental science in producing and managing resources efficiently, while ensuring safety and effectiveness in their applications.