1. The problem statement, all variables and given/known data Problem: Three common gaseous compounds of nitrogen an doxygen of different elementary composition are known, (A) laughing gas containing 63.65% nitrogen, (B) a colorless gas containing 46.68% nitrogen, and (C) a brown, toxic gas containing 30.45% nitrogen. Show how these data illustrate the law of multiple proportions. Solution: According to the law of multiple proportions, the relative amounts of an element combining with some fixed amount of a second element in a series of compounds are in ratios of small whole numbers. Since percent means “parts per hundred” we can assume 100 g. Then, on the basis of 100 g of each compound, we tabulate beow the mass of N, the mass of O (obtained b the difference from 100), and the mass of N per gram of O. Compound A Compound B Compound C g of N 63.65 46.68 30.45 g of O 36.35 53.32 69.55 (g of N)/(g of O) 1.7510 0.8755 0.4378 The relative amounts are not affected if all three amounts are set up in the form of a ratio and then divided by the smallest of the relative amounts. 1.7510: 0.8755 : 0.4378 = 1.7510/0.4378 : 0.8755/0.4378 : 0.4378/0.4378 = 4.000 : 2.000 : 1.000 The relative amounts are indeed the ratios of small whole numbers – 4.000 : 2.000 : 1.000 – within the precision of the analyses. The law of multiple proportions was an important contribution to the credibility of Dalton's atomic theory. It was discovered before relative atomic masses were well known (note that ##A_r## values were not involved in the calculation above.) However, it follows logically that all atoms of the same element have the same mass (which is unchangeable) and that compounds contain elements in the relative proportions of simple whole numbers. 2. Relevant equations 1) The use of percentages. 2) The use of ratios. 3. The attempt at a solution Towards the end of the solution, there is a mention of “##A_r##” values. What are these? Also, according to the law of multiple proportions “the relative amounts of an element combining with some FIXED AMOUNT OF A SECOND ELEMENT in a series of compounds are in ratios of small whole numbers.” The emphasized part from above holds because we fix the ratio of oxygen to be one gram (=the denominator of the fraction), right? If more information is needed, just ask. :) Any input would be appreciated!