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. Identify the percentage of nitrogen in the fertilizer, which is given as 15% by mass.
2. Convert the mass of the fertilizer from ounces to grams using the conversion factor: 1 oz = 28.3495 g.
3. Calculate the mass of nitrogen in the fertilizer by multiplying the total mass of the fertilizer in grams by the percentage of nitrogen (15%).
4. Set up the calculation as: (mass of fertilizer in grams) * (0.15) to find the mass of nitrogen.
5. Perform the multiplication to find the mass of nitrogen in grams.

Key Concepts

Mass Percentage

Mass percentage is a way to express 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 calculations are in compatible units.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another using conversion factors. It involves multiplying the quantity by conversion factors that cancel out the original units, leading to the desired units. This method is essential for solving the problem, as it allows for systematic conversion from ounces of fertilizer to grams of nitrogen.