EXAMPLE 2.1 Mass Ratios The gas methane (CH4), the main component of the fuel natural gas, can be decomposed to give carbon (C) and hydrogen (H) in a ratio of 3.00 parts by mass of carbon to 1.00 part by mass of hydrogen. How much hydrogen can be made from 90.0 g of methane? Solution We can express the parts ratio in any units we choose—pounds, grams, kilograms—as long as it is the same for both elements. Using grams as the units, we see that 3.00 g of C and 1.00 g of H would mean 4.00 g CH4 at the start. To convert g CH4 to g H, the conversion factor we need includes 1.00 g H and 4.00 g CH4. 90.0 g CH4 x = 22.5 g H 1.00 g H 4.00 g CH4 We multiply by the ratio, expressed in grams. We start with the given quantity. the number the unit The gas ammonia can be decomposed to give 3.00 parts by mass of hydrogen and 14.0 parts by mass of nitrogen. What mass of nitrogen is obtained if 1.27 g of ammonia is decomposed? Exercise 2.1A

EXAMPLE 2.1 Mass Ratios continued Exercise 2.1B Nitrous oxide, sometimes called “laughing gas,” can be decomposed to give 7.00 parts by mass of nitrogen and 4.00 parts by mass of oxygen. What mass of nitrogen is obtained if enough nitrous oxide is decomposed to yield 36.0 g of oxygen? Exercise 2.1B

EXAMPLE 2.2 Atom Ratios Hydrogen sulfide gas can be decomposed to give sulfur and hydrogen in a mass ratio of 16.0:1.00. If the relative mass of sulfur is 32.0 when the mass of hydrogen is taken to be 1.00, how many hydrogen atoms are combined with each sulfur atom in the gas? Solution x 3.2.0 units S 1 atom S 1.00 unit H 16.0 units S 1 atom H 1 unit H = 2 atoms H We start with the relative mass of a sulfur atom We multiply by the given mass ratio Then we multiply by the relative mass of a hydrogen atom The answer: a ratio of 2 atoms H to 1 atom S Arsine gas can be decomposed to give arsenic and hydrogen in a mass ratio of 25.0:1.00. If the relative mass of arsenic is 74.9 when the mass of hydrogen is taken to be 1.00, how many hydrogen atoms are combined with each arsenic atom in the gas? Exercise 2.2