Multiple choice

A mixture of $NH_{4}NO_{3}$ and $(NH_{4}){2}HPO{4}$ contains $30.40 \%$ mass percent of nitrogen. What is the mass ratio of the two components in the mixture?

  1. $2:1$
  2. $1:2$
  3. $3:4$
  4. $4:1$
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A Correct answer
Explanation

Nitrogen mass percent in NH4NO3 (MW=80) is 28/80 = 35%. In (NH4)2HPO4 (MW=132), it is 28/132 = 21.21%. Using the mixture rule: 30.40 - 21.21 = 9.19 and 35 - 30.40 = 4.60. The ratio is 9.19/4.60 which is approximately 2:1.

AI explanation

Let the mass of NH4NO3 be x and the mass of (NH4)2HPO4 be y. The molar mass of NH4NO3 is 80, giving it a nitrogen mass percentage of 35 percent. The molar mass of (NH4)2HPO4 is 132, giving it a nitrogen mass percentage of 21.2 percent. Using the method of alligation, the difference between the 35 percent nitrogen of NH4NO3 and the 30.40 percent mixture is 4.60 percent, while the difference between the 30.40 percent mixture and the 21.2 percent nitrogen of (NH4)2HPO4 is 9.20 percent. The ratio of the components is the inverse of these differences, which simplifies to 2:1.

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