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Numerade Educator



Problem 29 Medium Difficulty

The effectiveness of a nitrogen fertilizer is determined mainly by its mass $\%$ N. Rank the following fertilizers, most effective first: potassium nitrate; ammonium nitrate; ammonium sulfate; urea, $\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}$


1) urea
2) ammonium nitrate
3) ammonium sulfate
4) potassium nitrate


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Video Transcript

to find the percent nitrogen in a given compound. We look at how much nitrogen or the mass of nitrogen in one mole of the compound divided by the mass of one mole of the compound, which is the molar mass and then multiplied by 100 since it's expressed as a percent. So if we're given a compound potassium nitrate, the first step is to determine the chemical formula. Potassium is an eye on K plus, and nitrate is a poly atomic eye on an 03 with the minus. One charge, plus one and minus one means it's a 1 to 1 ratio, so the formula for potassium nitrate is K N 03 If we find the molar mass of potassium nitrate, it's the massive potassium, which we find on the periodic table. 39 0.98 plus the mass of nitrogen, 14.7 plus three times the mass of oxygen were 15 0.999 So those numbers all are the atomic masses found on the periodic table. In one mole of potassium nitrate, there's one nitrogen show in the top. We know there are 14.7 grams. So in one more potassium nitrate, there's 14.7 grams in the molar mass. This found by adding up all the numbers on the bottom to be 100 and one went 102 or 0.139 which is equal to 13.9%. So the percent nitrogen and potassium nitrate is 13.9%. Similarly, we have a compound ammonium nitrate. Ammonium nitrate is made up of the ammonium ion NH four plus in the nitrate ion and No. Three minus again a 1 to 1 ratio. So the formula is NH for n 03 To find the percent nature gin, we find the molar mass of the whole compound. There are two nitrogen, so it's two times 14 0.7 plus four hydrogen, four times 1.8 plus three oxygen's. So that's the molar mass of the whole compound. And in one mole there are two nitrogen ins, so there will be two times 14 point 007 grams, and this is 0.35 or 35%. Ammonium sulphate. Is there 1/3 compound made up of the ammonium ion with a plus one charge and the S 04 sulfate iron with a minus two charge. Because this is a minus two and this is a plus one, it means that there needs to be to ammonium ion for everyone sulfate. So the formula is NH for two eso for so my percent nitrogen is the molar mass of the whole compound. There are two nitrogen plus four times two or eight hydrogen plus one sulfur plus four oxygen's and the mass of nitrogen is two times 14.7 21%. The last compound is a compound called urea. We're given the chemical formula Kurban Times, oxygen and H for 22 So the percent this is called Yuria percent nitrogen is equal to. In this case, there are two. Nitrogen is in the whole compound, so my percent nitrogen will be too times the molar mass. I'm nitrogen and the mass of the whole compound is the massive carbon plus the mass of oxygen, plus two times the mass of nitrogen plus four. Because there are two times two hydrogen, this equals 40 7%. So in terms of percent, nitrogen area has the greatest, followed by ammonium nitrate, followed by ammonium sulphate, followed by potassium nitrate