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Chapter 1: Problem 53

A fertilizer contains \(21 \%\) nitrogen by mass. What mass of this fertilizer, in kilograms, is required for an application requiring \(225 \mathrm{g}\) of nitrogen?

Short Answer

Expert verified
The mass of fertilizer required for an application requiring 225 g of nitrogen is approximately 1.07 Kg.

Step by step solution

01

Convert Mass of Desired Nitrogen to Kilograms

225 g of nitrogen is equal to \(225 \div 1000 = 0.225\) Kg.
02

Calculate Required Mass of Fertilizer Using Proportions

Given that the fertilizer contains 21% nitrogen by mass, this means that if you have 1kg of the fertilizer, the mass of nitrogen in it would be 0.21Kg (since 21% of 1kg equals 0.21kg). So, to find the mass of the fertilizer that gives 0.225kg of nitrogen, set up a proportion and solve for x (mass of fertilizer). Thus: \( \frac{21}{100} : 1 = 0.225 : x \) , solving for x, yields \( x = \frac{1 \times 0.225}{0.21} \)
03

Final Result

After solving the proportion for x, the desired mass of fertilizer in kilograms is obtained.

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Most popular questions from this chapter

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