Solve each of the following problems using one or more conversion factors:
d. A plant fertilizer contains 15% nitrogen (N) by mass. In a container of soluble plant food, there are 10.0 oz of fertilizer. How many grams of nitrogen are in the container?

Verified step by step guidance

1. Step 1: Identify the given information. The fertilizer contains 15% nitrogen by mass, and the container has 10.0 oz of fertilizer. We need to calculate the mass of nitrogen in grams.
2. Step 2: Convert the mass of fertilizer from ounces to grams. Use the conversion factor: 1 oz = 28.3495 g. Multiply 10.0 oz by 28.3495 g/oz to find the mass of fertilizer in grams.
3. Step 3: Calculate the mass of nitrogen in the fertilizer. Since the fertilizer contains 15% nitrogen by mass, multiply the total mass of fertilizer (in grams) by 0.15 (representing 15%).
4. Step 4: Ensure the units are consistent throughout the calculation. The final result will be in grams of nitrogen.
5. Step 5: Double-check the calculation setup to confirm that the conversion factors and percentage are applied correctly.

Key Concepts

Mass Percentage

Mass percentage is a way of expressing the concentration of a component in a mixture. It is calculated by dividing the mass of the component by the total mass of the mixture and multiplying by 100. In this case, the fertilizer contains 15% nitrogen by mass, meaning that 15 grams of nitrogen are present in every 100 grams of fertilizer.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this problem, we need to convert ounces to grams to find the mass of nitrogen. Knowing that 1 ounce is approximately 28.35 grams allows us to perform this conversion accurately, ensuring that all measurements are in compatible units for calculation.

Calculating Mass of a Component

To find the mass of a specific component in a mixture, you multiply the total mass of the mixture by the mass percentage of that component. In this scenario, after converting the mass of fertilizer from ounces to grams, we can calculate the mass of nitrogen by applying the formula: mass of nitrogen = total mass of fertilizer × (mass percentage of nitrogen / 100). This step is crucial for determining the exact amount of nitrogen present.