Problem 39 - Chemistry: The Central Science in SI Units, Global Edition

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

The mass percentage of NaNO3 in the solution is 1.605%, and the concentration of chromium in the alloy is 28.6 ppm.

Step 1: Part (a) - Mass Percentage of NaNO3 in Solution

To calculate the mass percentage of NaNO3 in the solution, follow these steps: 1. Determine the mass of NaNO3: 13.6 g 2. Determine the mass of water: 834 g 3. Calculate the total mass of the solution: NaNO3 mass + water mass 4. Divide the mass of NaNO3 by the total mass of the solution. 5. Multiply the result by 100 to express it as a percentage. Let's calculate the mass percentage now: In this case, the mass of NaNO3 is 13.6 g, and the mass of water is 834 g. Total mass of the solution = 13.6 g (NaNO3) + 834 g (water) = 847.6 g Mass percentage of NaNO3 = \(\frac{13.6 \mathrm{~g}}{847.6 \mathrm{~g}}\) × 100

Step 2: Part (a) - Calculate Mass Percentage

Now, calculate the mass percentage: Mass percentage of NaNO3 = \(\frac{13.6}{847.6}\) × 100 = 1.605 % Hence, the mass percentage of NaNO3 in the solution is 1.605%.

Step 3: Part (b) - Chromium Concentration in Alloy

To calculate the concentration of chromium in the alloy in ppm, follow these steps: 1. Determine the mass of chromium: 2.86 g 2. Determine the mass of the alloy: 100 kg (convert to g) 3. Calculate the concentration of chromium in ppm. Let's calculate the concentration of chromium in ppm: In this case, the mass of chromium is 2.86 g and the mass of the alloy is 100 kg. Let's first convert the mass of alloy to g: Mass of the alloy = 100 kg × \(10^3 \mathrm{~g/kg}\) = 100,000 g Chromium concentration in ppm = \(\frac{2.86 \mathrm{~g}}{100,000 \mathrm{~g}}\) × \(10^6\)

Step 4: Part (b) - Calculate Chromium Concentration

Now, calculate the chromium concentration in ppm: Chromium concentration in ppm = \(\frac{2.86}{100,000}\) × \(10^6\) = 28.6 ppm Hence, the concentration of chromium in the alloy is 28.6 ppm.

Key Concepts

Solution Concentration

When talking about solution concentration, we are discussing how much of a certain substance, known as the solute, is present in a particular amount of solvent. A common way to express concentration is in percentages, like mass percentage.
This means we are looking at how much mass of the solute is in the total mass of the solution. For instance, in the problem with \(\mathrm{NaNO}_{3}\), we calculate its mass percentage by taking the mass of \(\mathrm{NaNO}_{3}\) and dividing it by the total mass of the entire mixture, then multiplying by 100 to convert it to a percentage.

• Mass of solute (NaNO3): 13.6 g
• Mass of solvent (water): 834 g
• Total mass of solution: 847.6 g

Here, the solution’s concentration is calculated based on these weighted proportions. The result tells us that 1.605% of the solution's mass is NaNO3.

PPM Calculation

PPM stands for parts per million, and it's a unit of measurement used to express very dilute concentrations of substances. It is akin to talking about one part of solute per one million parts of solution.
PPM is particularly useful when dealing with trace quantities of a substance and is often used in various fields including chemistry and environmental science.To effectively calculate the PPM of chromium in the alloy example given:

• Convert the mass of the alloy from kilograms to grams so that the units match with the grams of chromium.
• Determine the ratio of the chromium's mass to the mass of the alloy.
• Since we're looking for parts per million, we then multiply this fraction by \(10^6\).

Performing these steps gives us a concentration of 28.6 ppm, which signifies that in every million parts of the alloy, 28.6 parts are chromium.

Alloy Composition

Alloy composition is about understanding the different metallic elements combined to form an alloy. Each metal in the alloy contributes to its overall properties such as strength, malleability, or corrosion resistance.
Calculating the composition, such as the chromium content, helps in characterizing the material for its intended use.

• Think of alloys like mixtures that add beneficial qualities to the base metal.
• The concentration of an element like chromium might be expressed as a percentage or in parts per million (PPM) for more precision.

Understanding alloy composition is crucial for applications like manufacturing and material selection, where specific attributes are required. By knowing the concentration of elements like chromium, one can predict the performance and suitability of an alloy in various environmental or operational conditions.